cp's OEIS Frontend

A143719 Let n = Product_{p} p ^ e_p be the prime factorization of n and let M = max{e_p}. Then n is in the sequence iff for all primes q in the range 2 <= q <= M we have e_q >= Sum_{r} floor( log_q (e_r + 1) ).

%I A143719 #9 Jan 29 2025 22:11:50
%S A143719 1,2,3,4,5,6,7,10,11,12,13,14,15,17,19,20,21,22,23,24,26,28,29,30,31,
%T A143719 33,34,35,36,37,38,39,41,42,43,44,46,47,48,51,52,53,55,57,58,59,61,62,
%U A143719 65,66,67,68,69,70,71,72,73,74,76,77,78,79,82,83,85,86,87,89,91,92,93,94,95,97,100
%N A143719 Let n = Product_{p} p ^ e_p be the prime factorization of n and let M = max{e_p}. Then n is in the sequence iff for all primes q in the range 2 <= q <= M we have e_q >= Sum_{r} floor( log_q (e_r + 1) ).
%C A143719 A variant of A141586, which is a subsequence.
%H A143719 Robert Israel, <a href="/A143719/b143719.txt">Table of n, a(n) for n = 1..10000</a>
%p A143719 filter:= proc(n) local F,M;
%p A143719   F:= ifactors(n)[2];
%p A143719   M:= max(F[..,2]);
%p A143719   andmap(proc(q) local e; padic:-ordp(n,q) >= add(floor(log[q](e+1)),e=F[..,2]) end proc, select(isprime, [$2..M]))
%p A143719 end proc:
%p A143719 filter(1):= true:
%p A143719 select(filter, [$1..200]); # _Robert Israel_, Jan 29 2025
%Y A143719 Cf. A141586, A135130, A143720.
%K A143719 nonn
%O A143719 1,2
%A A143719 _N. J. A. Sloane_, Nov 29 2008