A354355 Characteristic function of numbers with their sum of divisors (sigma) 3-smooth.

1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for characteristic functions

Index entries for sequences related to sigma(n)

Formula

Multiplicative with a(p^e) = A065333(1 + p + p^2 + ... + p^e).

a(n) = A065333(A000203(n)).

Mathematica

a[n_] := If[Max @ FactorInteger[DivisorSigma[1, n]][[;; , 1]] <= 3, 1, 0]; Array[a, 100] (* Amiram Eldar, May 25 2022 *)

Prog

(PARI)
A065333(n) = ((3^valuation(n, 3)<<valuation(n, 2))==n); \\ From A065333
A354355(n) = A065333(sigma(n));

Crossrefs

Characteristic function of A354356.

Cf. A000203, A065333.

Cf. also A122255.

Sequence in context: A380467 A380524 A342005 * A266974 A075437 A130047

Adjacent sequences: A354352 A354353 A354354 * A354356 A354357 A354358

Keyword

nonn,mult

Author

Antti Karttunen, May 24 2022

Status

approved