A332422 - OEIS

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A332422

If n = Product (p_j^k_j) then a(n) = Sum ((-1)^(pi(p_j) + 1) * pi(p_j)), where pi = A000720.

0, 1, -2, 1, 3, -1, -4, 1, -2, 4, 5, -1, -6, -3, 1, 1, 7, -1, -8, 4, -6, 6, 9, -1, 3, -5, -2, -3, -10, 2, 11, 1, 3, 8, -1, -1, -12, -7, -8, 4, 13, -5, -14, 6, 1, 10, 15, -1, -4, 4, 5, -5, -16, -1, 8, -3, -10, -9, 17, 2, -18, 12, -6, 1, -3, 4, 19, 8, 7, 0, -20, -1

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OFFSET

1,3

COMMENTS

Sum of odd indices of distinct prime factors of n minus the sum of even indices of distinct prime factors of n.

LINKS

Table of n, a(n) for n=1..72.

Index entries for sequences computed from indices in prime factorization

FORMULA

G.f.: Sum_{k>=1} (-1)^(k + 1) * k * x^prime(k) / (1 - x^prime(k)).

EXAMPLE

a(66) = a(2 * 3 * 11) = a(prime(1) * prime(2) * prime(5)) = 1 - 2 + 5 = 4.