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A319273
Signed sum over the prime multiplicities of n.
3
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
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
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
(PARI) A319273(n) = if(1==n, n, my(f=factor(n)); sum(i=1, #f~, f[i, 2] * ((-1)^(i-1)))); \\ Antti Karttunen, Sep 30 2018
KEYWORD
sign
AUTHOR
Gus Wiseman, Sep 16 2018
EXTENSIONS
More terms from Antti Karttunen, Sep 30 2018
STATUS
approved