A382331 If n = Product (p_j^k_j) then a(n) = -Sum ((-1)^k_j * p_j).

0, 2, 3, -2, 5, 5, 7, 2, -3, 7, 11, 1, 13, 9, 8, -2, 17, -1, 19, 3, 10, 13, 23, 5, -5, 15, 3, 5, 29, 10, 31, 2, 14, 19, 12, -5, 37, 21, 16, 7, 41, 12, 43, 9, 2, 25, 47, 1, -7, -3, 20, 11, 53, 5, 16, 9, 22, 31, 59, 6, 61, 33, 4, -2, 18, 16, 67, 15, 26, 14, 71, -1, 73, 39, -2

Offset

1,2

Links

Table of n, a(n) for n=1..75.

Index entries for sequences computed from exponents in factorization of n.

Index entries for sequences computed from indices in prime factorization.

Formula

Additive with a(p^e) = (-1)^(e+1) * p.

Example

a(72) = a(2^3*3^2) = 2 - 3 = -1.

Mathematica

Join[{0}, Table[-Plus @@ ((-1)^#[[2]] #[[1]] & /@ FactorInteger[n]), {n, 2, 75}]]

Prog

(PARI) a(n) = my(f=factor(n)); -sum(i=1, #f~, (-1)^f[i, 2]*f[i, 1]); \\ Michel Marcus, Mar 22 2025

Crossrefs

Cf. A001414, A008472, A316523, A332422, A332423, A332424, A340901, A366749.

Sequence in context: A141346 A095402 A086294 * A361632 A075860 A361630

Adjacent sequences: A382328 A382329 A382330 * A382332 A382333 A382334

Keyword

sign,easy

Author

Ilya Gutkovskiy, Mar 22 2025

Status

approved