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

1,2

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

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]

Prog

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

Crossrefs

A387057 is a subsequence.

Cf. A033950, A037445, A048166.

Sequence in context: A215459 A019442 A048166 * A394288 A360013 A335738

Adjacent sequences: A387053 A387054 A387055 * A387057 A387058 A387059

Keyword

nonn,easy

Author

Amiram Eldar, Aug 15 2025

Status

approved