A391074 a(n) is the number of nonuniform divisors of n.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 3, 0, 1, 0, 1, 0, 2, 0, 2, 0, 0, 0, 3, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 4, 0, 0, 1, 1, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0, 2

Offset

1,24

Comments

This sequence first differs from A062977, A335460 and A376514 at n = 36: A062977(36) = 0, A335460(36) = 4, A376514(36) = 3 while a(36) = 2 = card({12, 18}).

Links

Felix Huber, Table of n, a(n) for n = 1..10000

Formula

a(n) = A000005(n) - A327527(n).

a(n) = A000005(n) - A034444(n) - A368251(n).

a(n) <= A376514(n).

Maple

A391074 := proc(n) local f, e, k, t, m, M; f := ifactors(n)[2]; e := map(l -> l[2], f); k := nops(f); M := max(e); t := 0; for m from 2 to M do t := t + 2^nops(select(x -> m <= x, e)) - 1; end do; return NumberTheory:-tau(n) - 2^k - t; end proc: seq(A391074(n), n = 1 .. 88);

Mathematica

a[n_] := Module[{e = FactorInteger[n][[;; , 2]]}, Times @@ (e+1) - 1 - Total[2^Accumulate[Count[e, #] & /@ Range[Max[e], 1, -1]] - 1]]; a[1] = 0; Array[a, 100] (* Amiram Eldar, Dec 03 2025 *)

Crossrefs

Cf. A000005, A034444, A051903, A062977, A327527, A335460, A368251, A376514.

Sequence in context: A072325 A294929 A391713 * A076948 A255309 A335446

Adjacent sequences: A391071 A391072 A391073 * A391075 A391076 A391077

Keyword

nonn,easy

Author

Felix Huber, Dec 03 2025

Extensions

Incorrect formula removed by Falk Hüffner, May 19 2026

Status

approved