A379473 a(n) is the highest power of 3 dividing the sum of divisors of n.

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

Offset: 1

Author

Antti Karttunen, Dec 27 2024

Keywords

• nonn
• mult

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to sigma(n).

Crossrefs

Cf. A000203, A000244, A038500, A354100, A379484 [= a(A379481(n))].

Cf. A329963 (positions of 1's), A087943 (of terms > 1).

Cf. also A082903.

Programs

Mathematica

a[n_] := 3^IntegerExponent[DivisorSigma[1, n], 3]; Array[a, 100] (* Amiram Eldar, Dec 27 2024 *)

PARI

A379473(n) = (3^valuation(sigma(n),3));

Formula

Multiplicative with a(p^e) = A038500((p^(e+1)-1)/(p-1)).

a(n) = A038500(A000203(n)).

a(n) = A000244(A354100(n)).