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

1,2

Links

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

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.

Mathematica

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

Prog

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

Crossrefs

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

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

Sequence in context: A203564 A369716 A365345 * A111575 A161836 A087576

Adjacent sequences: A375227 A375228 A375229 * A375231 A375232 A375233

Keyword

nonn,easy,mult

Author

Amiram Eldar, Aug 06 2024

Status

approved