A392628 The number of infinitary divisors of n that are numbers whose number of divisors is a power of 2.

1, 2, 2, 1, 2, 4, 2, 3, 1, 4, 2, 2, 2, 4, 4, 1, 2, 2, 2, 2, 4, 4, 2, 6, 1, 4, 3, 2, 2, 8, 2, 2, 4, 4, 4, 1, 2, 4, 4, 6, 2, 8, 2, 2, 2, 4, 2, 2, 1, 2, 4, 2, 2, 6, 4, 6, 4, 4, 2, 4, 2, 4, 2, 1, 4, 8, 2, 2, 4, 8, 2, 3, 2, 4, 2, 2, 4, 8, 2, 2, 1, 4, 2, 4, 4, 4, 4, 6, 2, 4

Offset

1,2

Comments

First differs from A295878, A363825 and A368470 at n = 32.

Links

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

Formula

Multiplicative with a(p^e) = A001511(e+1).

a(n) >= 1, with equality if and only if n is a square.

a(n) <= A037445(n), with equality if and only if n is squarefree (A005117).

Mathematica

f[p_, e_] := IntegerExponent[e + 1, 2] + 1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

Prog

(PARI) a(n) = vecprod(apply(x -> valuation(x+1, 2) + 1, factor(n)[, 2]));

Crossrefs

Cf. A001511, A005117, A036537, A037445, A077609, A372380, A392629, A392630.

Cf. A295878, A363825, A368470.

Sequence in context: A066954 A144925 A029262 * A363825 A368470 A295878

Adjacent sequences: A392625 A392626 A392627 * A392629 A392630 A392631

Keyword

nonn,mult,easy

Author

Amiram Eldar, Jan 18 2026

Status

approved