|
| |
|
|
A348477
|
|
Drop all 1 but the first 1 in A035306.
|
|
1
|
|
|
|
1, 2, 3, 2, 2, 5, 2, 3, 7, 2, 3, 3, 2, 2, 5, 11, 2, 2, 3, 13, 2, 7, 3, 5, 2, 4, 17, 2, 3, 2, 19, 2, 2, 5, 3, 7, 2, 11, 23, 2, 3, 3, 5, 2, 2, 13, 3, 3, 2, 2, 7, 29, 2, 3, 5, 31, 2, 5, 3, 11, 2, 17, 5, 7, 2, 2, 3, 2, 37, 2, 19, 3, 13, 2, 3, 5, 41, 2, 3, 7, 43, 2, 2, 11, 3, 2, 5, 2, 23, 47, 2, 4, 3, 7, 2, 2, 5, 2, 3, 17, 2, 2, 13, 53, 2, 3, 3, 5, 11, 2, 3, 7, 3, 19, 2, 29
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
List of prime divisors of n and their exponents, ignoring the exponent 1. - Michael De Vlieger, Oct 20 2021
|
|
|
LINKS
|
Seiichi Manyama, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Prime Factorization.
|
|
|
EXAMPLE
|
n prime factorization triangle
1 = 1. -> 1;
2 = 2. -> 2;
3 = 3. -> 3;
4 = 2^2. -> 2, 2;
5 = 5. -> 5;
6 = 2*3. -> 2, 3;
7 = 7. -> 7;
8 = 2^3. -> 2, 3;
9 = 3^2. -> 3, 2;
10 = 2*5. -> 2, 5;
11 = 11. -> 11;
12 = 2^2*3. -> 2, 2, 3;
13 = 13. -> 13;
14 = 2*7 -> 2, 7;
15 = 3*5. -> 3, 5;
16 = 2^4. -> 2, 4;
|
|
|
MATHEMATICA
|
Array[DeleteCases[Flatten@ FactorInteger[#], 1] &, 58] /. {} -> {1} // Flatten (* Michael De Vlieger, Oct 20 2021 *)
|
|
|
PROG
|
(PARI)
tabf(nn) = if(nn==1, print1(1, ", "), my(f=factor(nn)); for(i=1, #f~, for(j=1, 2, if((k=f[i, j])>j-1, print1(k, ", ")))));
(Ruby)
require 'prime'
def A348477(n)
ary = (2..n).map{|i| i.prime_division}.flatten
ary.delete(1)
[1] + ary
end
p A348477(60)
|
|
|
CROSSREFS
|
Column 1 is A020639.
Row lengths are A238949(n) for n > 1.
Cf. A027746, A035306.
Sequence in context: A207338 A027746 A307746 * A240230 A238689 A166454
Adjacent sequences: A348474 A348475 A348476 * A348478 A348479 A348480
|
|
|
KEYWORD
|
nonn,easy,tabf
|
|
|
AUTHOR
|
Seiichi Manyama, Oct 20 2021
|
|
|
STATUS
|
approved
|
| |
|
|
