A354100 The 3-adic valuation of sigma, sum of divisors function.

0, 1, 0, 0, 1, 1, 0, 1, 0, 2, 1, 0, 0, 1, 1, 0, 2, 1, 0, 1, 0, 2, 1, 1, 0, 1, 0, 0, 1, 2, 0, 2, 1, 3, 1, 0, 0, 1, 0, 2, 1, 1, 0, 1, 1, 2, 1, 0, 1, 1, 2, 0, 3, 1, 2, 1, 0, 2, 1, 1, 0, 1, 0, 0, 1, 2, 0, 2, 1, 2, 2, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 2, 1, 0, 3, 1, 1, 2, 2, 2, 0, 1, 0, 2, 1, 2, 0, 2, 1, 0, 1, 3, 0, 1, 1

Offset

1,10

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences related to sigma(n).

Formula

a(n) = A007949(A000203(n)).

Additive with a(p^e) = A007949((p^(e+1)-1)/(p-1)).

Mathematica

a[n_] := IntegerExponent[DivisorSigma[1, n], 3]; Array[a, 100] (* Amiram Eldar, May 18 2023 *)

Prog

(PARI) A354100(n) = valuation(sigma(n), 3);
(PARI) A354100(n) = { my(f=factor(n)); sum(k=1, #f~, valuation(((f[k, 1]^(f[k, 2]+1))-1)/(f[k, 1]-1), 3)); }; \\ Demonstrates the additivity

Crossrefs

Cf. A000203, A007949, A074941.

Cf. A329963 (positions of zeros), A087943 (of terms > 0).

Cf. also A336937, A354099.

Sequence in context: A321928 A321917 A115201 * A118229 A172250 A309047

Adjacent sequences: A354097 A354098 A354099 * A354101 A354102 A354103

Keyword

nonn

Author

Antti Karttunen, May 17 2022

Status

approved