A380457 Sum of divisors of n plus the number of distinct prime divisors of n: a(n) = sigma(n) + omega(n).

1, 4, 5, 8, 7, 14, 9, 16, 14, 20, 13, 30, 15, 26, 26, 32, 19, 41, 21, 44, 34, 38, 25, 62, 32, 44, 41, 58, 31, 75, 33, 64, 50, 56, 50, 93, 39, 62, 58, 92, 43, 99, 45, 86, 80, 74, 49, 126, 58, 95, 74, 100, 55, 122, 74, 122, 82, 92, 61, 171, 63, 98, 106, 128, 86, 147, 69, 128, 98, 147, 73, 197, 75, 116, 126, 142, 98, 171, 81, 188, 122, 128, 85, 227, 110, 134, 122

Offset: 1

Author

Wesley Ivan Hurt, Jun 22 2025

Keywords

• nonn
• easy
• changed

Comments

Inverse Möbius transform of A014683(n).

For each divisor d of n, add d+1 if d is prime, else add d.

Examples

			a(12) = 1 + (2+1) + (3+1) + 4 + 6 + 12 = 30.
		

Crossrefs

Cf. A000203 (sigma), A001221 (omega), A014683.

Programs

Mathematica

Table[DivisorSigma[1, n] + PrimeNu[n], {n, 100}]

Formula

a(n) = Sum_{d|n} A014683(d).

a(p^k) = (p^(k+1)+p-2)/(p-1) for p prime, k>=1. - Wesley Ivan Hurt, Jul 02 2025