22 (number)

22 (twenty-two) is the natural number following 21 and preceding 23.

In mathematics

Twenty-two is an even composite number, its proper divisors being 1, 2 and 11. 22 is the sixth discrete semiprime and the fourth in the (2 × q) family. With 21 it forms the second discrete semiprime pair. 22 has an aliquot sum of 14 and is the fifth composite number found in the 7-aliquot tree. It has a 7-member aliquot sequence 22, 14, 10, 8, 7, 1, 0 of which the next two members are themselves discrete semiprimes, 22 is the first discrete semiprime exhibiting this property. 169 also has 14 as its aliquot sum. 22 is itself the aliquot sum of two numbers 20, 38.

Twenty-two is a pentagonal number and a centered heptagonal number. When cutting a circle with just six line segments, the maximum number of pieces that can be so created is 22, thus 22 is a central polygonal number (see lazy caterer's sequence).

The sum of the totient function for the first eight integers is 22. 22 is a Perrin number, preceded in the sequence by 10, 12, 17.

22nd Derajat Mountain Battery (Frontier Force)

The 2nd Derajat Mountain Battery (Frontier Force) was an artillery battery in the British Indian Army. The battery was raised in 1851, from disbanded Sikh artillerymen following the Second Sikh War.

In 1857, one detachment saw service against mutineers in Oudh and Bundlekand in the Indian Rebellion of 1857. The Second Afghan War, saw the Derajat Mountain Battery with Lord Roberts throughout the war; from the Battle of Peiwar Kotal and the Siege of the Sherpur Cantonment and then on to that most famous march south to the Battle of Kandahar. After the war, in addition to numerous minor Frontier campaigns throughout the Century, the 2nd took part in the Chitral Expedition. When Major-General Low's was in charge of the relief of Chitral Fort in 1895, which was under siege after a local coup. Two years later it took part in the operations of the Tirah Campaign. To honour the visit of the Prince and Princess of Wales to Indian they took part in the Rawalpindi Parade 1905. In the Great War, the 2nd in 1916 joined the Indian Expeditionary Force B in the campaign against the Germans in German East Africa, where it would remain until the Armistice. After the war, the Battery saw service during the Third Afghan War of 1919, the Mohmand and Bajaur Operations (1933), Mohmand Campaign (1935) and operations in Waziristan against the Fakir of Ipi from 1936. In World War II they were part of the force sent to the East African Campaign.

22nd Air Landing Division (Wehrmacht)

The 22nd Infantry Division was a German infantry division in World War II.

History

Created as 22. Infanterie-Division in 1935, one regiment participated in the 1939 Invasion of Poland; the rest of the division stayed in garrison on the Siegfried Line in case of a French attack in defense of Poland. The division retrained as 22. Luftlande-Division (Air Landing Division) for rapid tactical deployment to captured enemy airbases and performed in that role during the invasion of the Netherlands suffering heavy losses, and afterward advanced into France operating as ordinary ground infantry. Though planned for use in its air-landing role for the Battle of Crete, it was replaced by another division at the last minute. It joined Army Group South in Operation Barbarossa (1941), attacking from Romania and, operating exclusively as ordinary ground infantry, helped storm Sevastopol in the Crimea (1942).

The unit was thereafter transferred to Crete for garrison duty and mop-up operations in the Aegean, playing a major role in the Battle of Leros. During September 1943, forces of the unit committed numerous atrocities in Viannos. On 26 April 1944 the divisional commander, Generalmajor Heinrich Kreipe, was abducted by a British Special Operations Executive team led by Major Patrick Leigh Fermor and Capt Bill Stanley Moss. Kreipe's car was ambushed at night on the way from the divisional headquarters at Ano Archanes to the Villa Ariadne at Knossos and he was taken cross-country over the mountains to the south coast where he and his captors were picked up by a British vessel near Rodakino on 14 May. This operation was later portrayed in the book Ill Met by Moonlight (1950) written by Moss based on his wartime diaries, later adapted as a film of the same name.