A351746 a(n) = Sum_{p|n, p prime} (p-1) * tau(n/p).

0, 1, 2, 2, 4, 6, 6, 3, 4, 10, 10, 10, 12, 14, 12, 4, 16, 11, 18, 16, 16, 22, 22, 14, 8, 26, 6, 22, 28, 28, 30, 5, 24, 34, 20, 18, 36, 38, 28, 22, 40, 36, 42, 34, 20, 46, 46, 18, 12, 19, 36, 40, 52, 16, 28, 30, 40, 58, 58, 44, 60, 62, 26, 6, 32, 52, 66, 52, 48, 44, 70, 25, 72, 74

Offset: 1

Author

Wesley Ivan Hurt, Feb 17 2022

Keywords

• nonn

Examples

			a(12) = 10; a(12) = Sum_{p|12, p prime} (p-1) * tau(12/p) = (2-1)*tau(12/2) + (3-1)*tau(12/3) = tau(6) + 2*tau(4) = 4 + 2*3 = 10.
		

Crossrefs

Cf. A000005 (tau), A001221 (omega), A248577, A351711.

Programs

PARI

a(n) = my(f=factor(n)); sum(k=1, #f~, (f[k,1]-1)*numdiv(n/f[k,1])); \\ Michel Marcus, Feb 18 2022

Formula

a(n) = A351711(n) - A248577(n).