|
|
A061395
|
|
Let p be the largest prime factor of n; if p is the k-th prime then set a(n) = k; a(1) = 0 by convention.
|
|
311
|
|
|
0, 1, 2, 1, 3, 2, 4, 1, 2, 3, 5, 2, 6, 4, 3, 1, 7, 2, 8, 3, 4, 5, 9, 2, 3, 6, 2, 4, 10, 3, 11, 1, 5, 7, 4, 2, 12, 8, 6, 3, 13, 4, 14, 5, 3, 9, 15, 2, 4, 3, 7, 6, 16, 2, 5, 4, 8, 10, 17, 3, 18, 11, 4, 1, 6, 5, 19, 7, 9, 4, 20, 2, 21, 12, 3, 8, 5, 6, 22, 3, 2, 13, 23, 4, 7, 14, 10, 5, 24, 3, 6, 9, 11, 15
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
Records occur at the primes. - Robert G. Wilson v, Dec 30 2007
For n > 1: length of n-th row in A067255. - Reinhard Zumkeller, Jun 11 2013
a(n) = the largest part of the partition having Heinz number n. We define the Heinz number of a partition p = [p_1, p_2, ..., p_r] as Product(p_j-th prime, j=1...r) (concept used by Alois P. Heinz in A215366 as an "encoding" of a partition). For example, for the partition [1, 1, 2, 4, 10] we get 2*2*3*7*29 = 2436. Example: a(20) = 3; indeed, the partition having Heinz number 20 = 2*2*5 is [1,1,3]. - Emeric Deutsch, Jun 04 2015
|
|
LINKS
|
Álvar Ibeas, Table of n, a(n) for n = 1..100000 (first 1000 terms from Harry J. Smith)
Index entries for sequences computed from indices in prime factorization
|
|
FORMULA
|
A000040(a(n)) = A006530(n); a(n) = A049084(A006530(n)). - Reinhard Zumkeller, May 22 2003
A243055(n) = a(n) - A055396(n). - Antti Karttunen, Mar 07 2017
a(n) = A000720(A006530(n)). - Alois P. Heinz, Mar 05 2020
|
|
EXAMPLE
|
a(20) = 3 since the largest prime factor of 20 is 5, which is the 3rd prime.
|
|
MAPLE
|
with(numtheory):
a:= n-> pi(max(1, factorset(n)[])):
seq(a(n), n=1..100); # Alois P. Heinz, Aug 03 2013
|
|
MATHEMATICA
|
Insert[Table[PrimePi[FactorInteger[n][[ -1]][[1]]], {n, 2, 120}], 0, 1] (* Stefan Steinerberger, Apr 11 2006 *)
f[n_] := PrimePi[ FactorInteger@n][[ -1, 1]]; Array[f, 94] (* Robert G. Wilson v, Dec 30 2007 *)
|
|
PROG
|
(PARI) { for (n=1, 1000, if (n==1, a=0, f=factor(n)~; p=f[1, length(f)]; a=primepi(p)); write("b061395.txt", n, " ", a) ) } \\ Harry J. Smith, Jul 22 2009
(PARI) a(n) = if (n==1, 0, primepi(vecmax(factor(n)[, 1]))); \\ Michel Marcus, Nov 14 2022
(Haskell)
a061395 = a049084 . a006530 -- Reinhard Zumkeller, Jun 11 2013
(Python)
from sympy import primepi, primefactors
def a(n): return 0 if n==1 else primepi(primefactors(n)[-1])
print([a(n) for n in range(1, 101)]) # Indranil Ghosh, May 14 2017
|
|
CROSSREFS
|
Cf. A000720, A006530, A055396, A061394, A133674, A243055.
Sequence in context: A324729 A355532 A253558 * A290103 A156061 A225395
Adjacent sequences: A061392 A061393 A061394 * A061396 A061397 A061398
|
|
KEYWORD
|
easy,nice,nonn
|
|
AUTHOR
|
Henry Bottomley, Apr 30 2001
|
|
EXTENSIONS
|
Definition reworded by N. J. A. Sloane, Jul 01 2008
|
|
STATUS
|
approved
|
|
|
|