A318304 a(n) = A083254(n)/A003557(n) = (2*A173557(n) - A007947(n)).

1, 0, 1, 0, 3, -2, 5, 0, 1, -2, 9, -2, 11, -2, 1, 0, 15, -2, 17, -2, 3, -2, 21, -2, 3, -2, 1, -2, 27, -14, 29, 0, 7, -2, 13, -2, 35, -2, 9, -2, 39, -18, 41, -2, 1, -2, 45, -2, 5, -2, 13, -2, 51, -2, 25, -2, 15, -2, 57, -14, 59, -2, 3, 0, 31, -26, 65, -2, 19, -22, 69, -2, 71, -2, 1, -2, 43, -30, 77, -2, 1, -2, 81, -18, 43, -2, 25

Offset: 1

Author

Antti Karttunen, Aug 26 2018

Keywords

• sign

Links

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

Crossrefs

Cf. A000010, A003557, A007947, A083254, A173557, A318305.

Cf. A065463, A307868.

Programs

PARI

A173557(n) = my(f=factor(n)[, 1]); prod(k=1, #f, f[k]-1); \\ From A173557
A007947(n) = factorback(factorint(n)[, 1]); \\ From A007947
A318304(n) = (2*A173557(n) - A007947(n));

PARI

A083254(n) = (2*eulerphi(n)-n);
A003557(n) = { my(f=factor(n)); for (i=1, #f~, f[i, 2] = f[i, 2]-1); factorback(f); }; \\ From A003557
A318304(n) = (A083254(n)/A003557(n));

Formula

a(n) = A083254(n)/A003557(n) = 2*A173557(n) - A007947(n).

a(n) = A173557(n) - A318305(n).

Sum_{k=1..n} a(k) ~ c * n^2 / 2, where c = 2 * A307868 - A065463 = 0.238919... . - Amiram Eldar, Dec 07 2023