A332425 If n = Product (p_j^k_j) then a(n) = Sum ((-1)^(pi(p_j) + 1) * p_j * k_j), where pi = A000720.

0, 2, -3, 4, 5, -1, -7, 6, -6, 7, 11, 1, -13, -5, 2, 8, 17, -4, -19, 9, -10, 13, 23, 3, 10, -11, -9, -3, -29, 4, 31, 10, 8, 19, -2, -2, -37, -17, -16, 11, 41, -8, -43, 15, -1, 25, 47, 5, -14, 12, 14, -9, -53, -7, 16, -1, -22, -27, 59, 6, -61, 33, -13, 12, -8, 10, 67, 21, 20

Offset

1,2

Comments

Sum of prime factors of n (counted with multiplicity) with odd indices minus the sum of prime factors of n (counted with multiplicity) with even indices.

Links

Table of n, a(n) for n=1..69.

Index entries for sequences computed from indices in prime factorization

Example

a(252) = a(2^2 * 3^2 * 7) = a(prime(1)^2 * prime(2)^2 * prime(4)) = 2 + 2 - 3 - 3 - 7 = -9.

Mathematica

a[n_] := Plus @@ ((-1)^(PrimePi[#[[1]]] + 1) #[[1]] #[[2]] & /@ FactorInteger[n]); a[1] = 0; Table[a[n], {n, 1, 69}]

Crossrefs

Cf. A000720, A001414, A002129, A071321, A112798, A195017, A325699, A332424.

Sequence in context: A082299 A081806 A059806 * A286594 A241479 A100994

Adjacent sequences: A332422 A332423 A332424 * A332426 A332427 A332428

Keyword

sign

Author

Ilya Gutkovskiy, Feb 12 2020

Status

approved