A382477 If n = Product (p_j^k_j) then a(n) = -Sum ((-1)^k_j * k_j * p_j).
0, 2, 3, -4, 5, 5, 7, 6, -6, 7, 11, -1, 13, 9, 8, -8, 17, -4, 19, 1, 10, 13, 23, 9, -10, 15, 9, 3, 29, 10, 31, 10, 14, 19, 12, -10, 37, 21, 16, 11, 41, 12, 43, 7, -1, 25, 47, -5, -14, -8, 20, 9, 53, 11, 16, 13, 22, 31, 59, 4, 61, 33, 1, -12, 18, 16, 67, 13, 26, 14, 71, 0, 73, 39, -7
Offset: 1
Keywords
Examples
a(72) = a(2^3*3^2) = 3*2 - 2*3 = 0.
Programs
-
Mathematica
Join[{0}, Table[-Plus @@ ((-1)^#[[2]] #[[2]] #[[1]] & /@ FactorInteger[n]), {n, 2, 75}]] -
PARI
a(n) = my(f=factor(n)); -sum(k=1, #f~, (-1)^f[k,2]*f[k,2]*f[k,1]); \\ Michel Marcus, Apr 17 2025