A344461 a(n) = Sum_{d|n} d^gcd(d,n/d).

1, 3, 4, 9, 6, 12, 8, 29, 37, 18, 12, 60, 14, 24, 24, 341, 18, 273, 20, 134, 32, 36, 24, 236, 3151, 42, 784, 240, 30, 72, 32, 4645, 48, 54, 48, 48789, 38, 60, 56, 574, 42, 96, 44, 548, 3462, 72, 48, 21740, 823593, 103203, 72, 750, 54, 6888, 72, 1072, 80, 90, 60, 1160

Offset: 1

Author

Wesley Ivan Hurt, May 19 2021

Keywords

• nonn

Comments

If p is prime, a(p) = Sum_{d|p} d^gcd(d,p/d) = 1^1 + p^1 = p + 1.

Examples

			a(8) = Sum_{d|8} d^gcd(d,8/d) = 1^1 + 2^2 + 4^2 + 8^1 = 29.
		

Crossrefs

Cf. A055155, A337180.

Programs

Mathematica

Table[Sum[k^GCD[k, n/k] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 80}]