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) ).

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, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 46, 47, 48, 51, 52, 53, 55, 57, 58, 59, 61, 62, 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

Offset: 1

Author

N. J. A. Sloane, Nov 29 2008

Keywords

• nonn

Comments

A variant of A141586, which is a subsequence.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A141586, A135130, A143720.

Programs

Maple

filter:= proc(n) local F,M;
  F:= ifactors(n)[2];
  M:= max(F[..,2]);
  andmap(proc(q) local e; padic:-ordp(n,q) >= add(floor(log[q](e+1)),e=F[..,2]) end proc, select(isprime, [$2..M]))
end proc:
filter(1):= true:
select(filter, [$1..200]); # Robert Israel, Jan 29 2025