A242031 Numbers n such that prime factorization n = p_1^k_1*p_2^k_2*...*p_r^k_r satisfies k_1 >= k_2 >= ... >= k_r.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72

Offset: 1

Author

Jean-François Alcover, Aug 14 2014

Keywords

• nonn

Comments

Complement sequence begins 18, 50, 54, 75, 90, 98, ... (A071365).

Examples

			12 = 2^2*3^1 is in the sequence, but 18 = 2^1*3^2 is not.
		

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A071365, A304686 (strictly decreasing).

Programs

Maple

filter:= proc(n)
local F;
F:= ifactors(n)[2];
F:= sort(F,(s,t) -> s[1]>t[1]);
ListTools:-Sorted(map(t -> t[2],F));
end:
select(filter, [$1..100]); # Robert Israel, Aug 18 2014

Mathematica

Select[Range[100], GreaterEqual @@ (FactorInteger[#][[All, 2]]) &]

PARI

s=[]; for(n=1, 10^3, m=factor(n)[,2]; if(vecsort(m,,4)==m, s=concat(s, n))); s \\ Jens Kruse Andersen, Aug 18 2014