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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.

%I A242031 #50 Jul 11 2020 23:45:24
%S A242031 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 A242031 28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,51,
%U A242031 52,53,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72
%N 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.
%C A242031 Complement sequence begins 18, 50, 54, 75, 90, 98, ... (A071365).
%H A242031 Jens Kruse Andersen, <a href="/A242031/b242031.txt">Table of n, a(n) for n = 1..10000</a>
%e A242031 12 = 2^2*3^1 is in the sequence, but 18 = 2^1*3^2 is not.
%p A242031 filter:= proc(n)
%p A242031 local F;
%p A242031 F:= ifactors(n)[2];
%p A242031 F:= sort(F,(s,t) -> s[1]>t[1]);
%p A242031 ListTools:-Sorted(map(t -> t[2],F));
%p A242031 end:
%p A242031 select(filter, [$1..100]); # _Robert Israel_, Aug 18 2014
%t A242031 Select[Range[100], GreaterEqual @@ (FactorInteger[#][[All, 2]]) &]
%o A242031 (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 A242031 Cf. A071365, A304686 (strictly decreasing).
%K A242031 nonn
%O A242031 1,2
%A A242031 _Jean-François Alcover_, Aug 14 2014