A323154 - OEIS

A323154

a(n) = 1 if n divides A048146(n) = (sigma(n)-usigma(n)), 0 otherwise.

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

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OFFSET

COMMENTS

Characteristic function of A064594.

a(n) = 1 if and only if n divides A048146(n) = (A000203(n) - A034448(n)).

Differs from A008966 at n = 24, 112, 1984, 2520, 31320, 32512, ... (A064595).

LINKS

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

Index entries for characteristic functions.

MATHEMATICA

f[p_, e_] := (p^(e+1)-1)/(p-1); a[n_] := Module[{fct = FactorInteger[n]}, If[Divisible[Times @@ f @@@ fct - Times @@ (1 + Power @@@ fct), n], 1, 0]]; a[1] = 1; Array[a, 100] (* Amiram Eldar, Aug 25 2026 *)

PROG

(PARI)

A034448(n) = { my(f=factorint(n)); prod(k=1, #f~, 1+(f[k, 1]^f[k, 2])); }; \\ After code in A034448

A323154(n) = !((sigma(n)-A034448(n))%n);

CROSSREFS

Cf. A000203, A008966, A034448, A048146, A064594, A064595.

Sequence in context: A353559 A253206 A133639 * A060038 A197774 A219009

Adjacent sequences: A323151 A323152 A323153 * A323155 A323156 A323157

KEYWORD

nonn,easy,changed

AUTHOR

Antti Karttunen, Jan 09 2019

STATUS

approved