A387056 Numbers k that are divisible by the number of infinitary divisors of k.

1, 2, 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 64, 68, 72, 76, 80, 88, 92, 96, 100, 104, 112, 116, 124, 128, 136, 144, 148, 152, 160, 164, 172, 176, 184, 188, 192, 196, 200, 208, 212, 224, 232, 236, 240, 244, 248, 256, 268, 272, 284, 288, 292, 296

Offset: 1

Author

Amiram Eldar, Aug 15 2025

Keywords

• nonn
• easy

Comments

First differs from A048166 at n = 27: A048166(27) = 108 is not a term of this sequence.

This sequence is infinite. For example, if p is a prime, then 8*p is a term.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

A387057 is a subsequence.

Cf. A033950, A037445, A048166.

Programs

Mathematica

f[p_, e_] := 2^DigitCount[e, 2, 1]; id[1] = 1; id[n_] := Times @@ f @@@ FactorInteger[n]; q[k_] := Divisible[k, id[k]]; Select[Range[300], q]

PARI

isok(k) = !(k % vecprod(apply(x -> 2^hammingweight(x), factor(k)[, 2])));