A319273 - OEIS

A319273

Signed sum over the prime multiplicities of n.

1, 1, 1, 2, 1, 0, 1, 3, 2, 0, 1, 1, 1, 0, 0, 4, 1, -1, 1, 1, 0, 0, 1, 2, 2, 0, 3, 1, 1, 1, 1, 5, 0, 0, 0, 0, 1, 0, 0, 2, 1, 1, 1, 1, 1, 0, 1, 3, 2, -1, 0, 1, 1, -2, 0, 2, 0, 0, 1, 2, 1, 0, 1, 6, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, -1, 1, 0, 1, 1, 3, 4, 0, 1, 2, 0, 0, 0, 2, 1, 0, 0, 1, 0, 0, 0, 4, 1, -1, 1, 0, 1, 1, 1, 2, 1

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OFFSET

1,4

COMMENTS

If n = Product prime(x_i)^y_i is the prime factorization of n, then a(n) = Sum (-1)^(i-1) y_i.

LINKS

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

EXAMPLE

The prime factorization of 810 is 2^1 * 3^4 * 5^1, so a(810) = 1 - 4 + 1 = -2.

MATHEMATICA

Table[Total[MapIndexed[(-1)^(#2[[1]]-1)*#1&, Last/@FactorInteger[n]]], {n, 100}]

PROG