A333177 - OEIS

A333177

a(n) = Sum_{d|n, gcd(d, n/d) = 1} (-1)^omega(n/d) * prime(d).

2, 1, 3, 5, 9, 7, 15, 17, 21, 17, 29, 27, 39, 25, 33, 51, 57, 37, 65, 55, 53, 47, 81, 67, 95, 59, 101, 85, 107, 41, 125, 129, 103, 79, 123, 123, 155, 95, 123, 145, 177, 75, 189, 157, 165, 115, 209, 167, 225, 131, 171, 193, 239, 147, 217, 229, 199, 161, 275, 147

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OFFSET

1,1

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

Sum_{d|n, gcd(d, n/d) = 1} a(d) = prime(n).

MAPLE

f:= proc(n) local F, t, D, d;

F:= map(t -> t[1]^t[2], ifactors(n)[2]);

D:= map(convert, combinat:-powerset(F), `*`);

add((-1)^NumberTheory:-Omega(n/d, distinct)*ithprime(d), d=D)