A242031 - OEIS

%I #50 Jul 11 2020 23:45:24

%S 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,

%T 28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,51,

%U 52,53,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72

%N 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.

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

%H Jens Kruse Andersen, <a href="/A242031/b242031.txt">Table of n, a(n) for n = 1..10000</a>

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

%p filter:= proc(n)

%p local F;

%p F:= ifactors(n)[2];

%p F:= sort(F,(s,t) -> s[1]>t[1]);

%p ListTools:-Sorted(map(t -> t[2],F));

%p end:

%p select(filter, [$1..100]); # _Robert Israel_, Aug 18 2014

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

%o (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

%Y Cf. A071365, A304686 (strictly decreasing).

%K nonn

%O 1,2

%A _Jean-François Alcover_, Aug 14 2014