A385628 Sum of the divisors d of n with an even number of primes not exceeding d.

1, 1, 4, 5, 1, 4, 8, 13, 13, 11, 1, 8, 14, 22, 19, 29, 1, 13, 20, 35, 32, 23, 1, 16, 1, 14, 13, 26, 30, 59, 1, 29, 4, 1, 8, 17, 38, 58, 56, 83, 1, 46, 44, 71, 73, 47, 1, 32, 8, 11, 4, 18, 54, 67, 56, 90, 80, 88, 1, 83, 62, 63, 104, 93, 79, 92, 1, 5, 4, 32, 72, 97, 1, 38, 19, 62, 8, 56, 80, 179, 94, 83, 1, 50, 1, 44, 33, 79, 90, 203, 112, 143, 97, 95, 115

Offset: 1

Author

Wesley Ivan Hurt, Jul 05 2025

Keywords

• nonn
• easy

Comments

Inverse Möbius transform of n * ((pi(n)+1) mod 2) = n * A131377(n).

Examples

			The sum of the divisors d of 16 such that pi(d) is even gives 1 + 4 + 8 + 16 = 29.
		

Crossrefs

Cf. A000203 (sigma), A000720 (pi), A131377, A345220, A385625.

Programs

Mathematica

Table[Sum[d*Mod[PrimePi[d] + 1, 2], {d, Divisors[n]}], {n, 100}]

Formula

a(n) = Sum_{d|n} d * ((pi(d)+1) mod 2).

a(n) = A000203(n) - A385625(n).