A323159 Greatest common divisor of product (1+(p^e)) and product (1+p), where p ranges over prime factors of n, with e corresponding exponent; a(n) = gcd(A034448(n), A048250(n)).

1, 3, 4, 1, 6, 12, 8, 3, 2, 18, 12, 4, 14, 24, 24, 1, 18, 6, 20, 6, 32, 36, 24, 12, 2, 42, 4, 8, 30, 72, 32, 3, 48, 54, 48, 2, 38, 60, 56, 18, 42, 96, 44, 12, 12, 72, 48, 4, 2, 6, 72, 14, 54, 12, 72, 24, 80, 90, 60, 24, 62, 96, 16, 1, 84, 144, 68, 18, 96, 144, 72, 6, 74, 114, 8, 20, 96, 168, 80, 6, 2, 126, 84, 32, 108, 132, 120, 36, 90, 36

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..16384

Formula

a(n) = gcd(A034448(n), A048250(n)).

Mathematica

A323159[n_] := If[n == 1, 1, GCD[Times @@ (Power @@@ # + 1), Times @@ (#[[All, 1]] + 1)] & [FactorInteger[n]]];
Array[A323159, 100] (* Paolo Xausa, Oct 07 2025 *)

Prog

(PARI)
A034448(n) = { my(f=factorint(n)); prod(k=1, #f~, 1+(f[k, 1]^f[k, 2])); }; \\ After code in A034448
A048250(n) = factorback(apply(p -> p+1, factor(n)[, 1]));
A323159(n) = gcd(A034448(n), A048250(n));

Crossrefs

Cf. A034448, A048250, A323160, A323163.

Sequence in context: A348047 A348984 A389204 * A347090 A328181 A358346

Adjacent sequences: A323156 A323157 A323158 * A323160 A323161 A323162

Keyword

nonn

Author

Antti Karttunen, Jan 09 2019

Status

approved