A355940 a(n) = 1 if A003973(n) is a multiple of A000203(n), otherwise 0.

1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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 computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

a(n) = [A355934(n) == 1], where [ ] is the Iverson bracket.

Mathematica

f[p_, e_] := ((q = NextPrime[p])^(e + 1) - 1)/(q - 1); a[1] = 1; a[n_] := If[Divisible[Times @@ f @@@ FactorInteger[n], DivisorSigma[1, n]], 1, 0]; Array[a, 100] (* Amiram Eldar, Jul 22 2022 *)

Prog

(PARI)
A003973(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); sigma(factorback(f)); };
A355940(n) = !(A003973(n)%sigma(n));

Crossrefs

Characteristic function of A355941.

Cf. A000203, A003973, A355934.

Sequence in context: A358750 A205809 A353370 * A348033 A327153 A133943

Adjacent sequences: A355937 A355938 A355939 * A355941 A355942 A355943

Keyword

nonn

Author

Antti Karttunen, Jul 22 2022

Status

approved