A323159 - OEIS

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

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OFFSET

1,2

LINKS

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

FORMULA

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

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));