A345373 Sum of the divisor complements of the unitary prime divisors of n.

0, 1, 1, 0, 1, 5, 1, 0, 0, 7, 1, 4, 1, 9, 8, 0, 1, 9, 1, 4, 10, 13, 1, 8, 0, 15, 0, 4, 1, 31, 1, 0, 14, 19, 12, 0, 1, 21, 16, 8, 1, 41, 1, 4, 9, 25, 1, 16, 0, 25, 20, 4, 1, 27, 16, 8, 22, 31, 1, 32, 1, 33, 9, 0, 18, 61, 1, 4, 26, 59, 1, 0, 1, 39, 25, 4, 18, 71, 1, 16, 0, 43

Offset: 1

Author

Wesley Ivan Hurt, Jun 16 2021

Keywords

• nonn

Comments

a(p) = 1 for p prime.

Examples

			a(30) = 30 * Sum_{p|30, p prime} floor(1/gcd(p,30/p))/p = 30 * (1/2 + 1/3 + 1/5) = 31.
		

Crossrefs

Cf. A063956.

Formula

a(n) = n * Sum_{p|n, p prime} floor(1/gcd(p,n/p)) / p.