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A375230
The total number of infinitary divisors of the infinitary divisors of n.
1
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
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
Similar sequences: A007425 (analogous with all the divisors), A074816 (unitary analog).
Sequence in context: A203564 A369716 A365345 * A111575 A161836 A087576
KEYWORD
nonn,easy,mult
AUTHOR
Amiram Eldar, Aug 06 2024
STATUS
approved