A363825 The number of infinitary divisors of n that are exponentially odd numbers (A268335).

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, 3, 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

Offset

1,2

Comments

First differs from A295878 at n = 32.

Links

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

Formula

Multiplicative with a(p^e) = 1 if e is even, and a(p^e) = 2^A000120(e-1) + 1 if e is odd.

a(n) <= A000005(n) with equality if and only if n is squarefree (A005117).

Mathematica

f[p_, e_] := 1 + If[OddQ[e], 2^DigitCount[e-1, 2, 1], 0]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

Prog

(PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, if(f[i, 2]%2, 2^hammingweight(f[i, 2]-1) + 1, 1))};

Crossrefs

Cf. A000005, A000120, A005117, A037445, A077609, A268335, A295878, A358260.

Sequence in context: A066954 A144925 A029262 * A368470 A295878 A368977

Adjacent sequences: A363822 A363823 A363824 * A363826 A363827 A363828

Keyword

nonn,easy,mult

Author

Amiram Eldar, Oct 19 2023

Status

approved