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

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences related to sigma(n).

Formula

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

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

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

Mathematica

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

Prog

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

Crossrefs

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

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

Cf. also A082903.

Sequence in context: A134444 A176149 A091442 * A025834 A257379 A336456

Adjacent sequences: A379470 A379471 A379472 * A379474 A379475 A379476

Keyword

nonn,mult

Author

Antti Karttunen, Dec 27 2024

Status

approved