A375230 The total number of infinitary divisors of the infinitary divisors of n.

1, 3, 3, 3, 3, 9, 3, 9, 3, 9, 3, 9, 3, 9, 9, 3, 3, 9, 3, 9, 9, 9, 3, 27, 3, 9, 9, 9, 3, 27, 3, 9, 9, 9, 9, 9, 3, 9, 9, 27, 3, 27, 3, 9, 9, 9, 3, 9, 3, 9, 9, 9, 3, 27, 9, 27, 9, 9, 3, 27, 3, 9, 9, 9, 9, 27, 3, 9, 9, 27, 3, 27, 3, 9, 9, 9, 9, 27, 3, 9, 3, 9, 3, 27

Offset: 1

Author

Amiram Eldar, Aug 06 2024

Keywords

• nonn
• easy
• mult

Links

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

Crossrefs

Cf. A000120, A005117, A037445, A064547, A077609, A138302.

Similar sequences: A007425 (analogous with all the divisors), A074816 (unitary analog).

Programs

Mathematica

f[p_, e_] := 3^DigitCount[e, 2, 1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100]

PARI

a(n) = vecprod(apply(x -> 3^hammingweight(x), factor(n)[,2]));

Formula

a(n) = Sum_{d infinitary divisor of n} A037445(d).

Multiplicative with a(p^e) = 3^A000120(e).

a(n) = 3^A064547(n).

a(n) = A007425(n) if and only if n is squarefree (A005117).

a(n) = A074816(n) if and only if n is in A138302.