A373364 - OEIS

A373364

a(n) = gcd(A001414(n), A003415(n)), where A001414 is the sum of prime factors with repetition, and A003415 is the arithmetic derivative.

0, 1, 1, 4, 1, 5, 1, 6, 6, 7, 1, 1, 1, 9, 8, 8, 1, 1, 1, 3, 10, 13, 1, 1, 10, 15, 9, 1, 1, 1, 1, 10, 14, 19, 12, 10, 1, 21, 16, 1, 1, 1, 1, 3, 1, 25, 1, 1, 14, 3, 20, 1, 1, 1, 16, 1, 22, 31, 1, 4, 1, 33, 1, 12, 18, 1, 1, 3, 26, 1, 1, 12, 1, 39, 1, 1, 18, 1, 1, 1, 12, 43, 1, 2, 22, 45, 32, 1, 1, 1, 20, 3, 34, 49, 24

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OFFSET

1,4

COMMENTS

For n >= 1, a(n) is a multiple of A373363(n).

LINKS

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

PROG

(PARI)

A001414(n) = ((n=factor(n))[, 1]~*n[, 2]); \\ From A001414.

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));

A373364(n) = gcd(A001414(n), A003415(n));