A345310 a(n) = Sum_{p|n, p prime} p^gcd(p,n/p).

0, 2, 3, 4, 5, 5, 7, 4, 27, 7, 11, 7, 13, 9, 8, 4, 17, 29, 19, 9, 10, 13, 23, 7, 3125, 15, 27, 11, 29, 10, 31, 4, 14, 19, 12, 31, 37, 21, 16, 9, 41, 12, 43, 15, 32, 25, 47, 7, 823543, 3127, 20, 17, 53, 29, 16, 11, 22, 31, 59, 12, 61, 33, 34, 4, 18, 16, 67, 21, 26, 14, 71, 31

Offset

1,2

Comments

a(p) = Sum_{p|p} p^gcd(p,p/p) = p^1 = p, for p prime.

Links

Table of n, a(n) for n=1..72.

Example

a(18) = Sum_{p|18} p^gcd(p,18/p) = 2^gcd(2,9) + 3^gcd(3,6) = 2^1 + 3^3 = 29.

Mathematica

Table[Sum[k^GCD[k, n/k] (PrimePi[k] - PrimePi[k - 1]) (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 100}]

Crossrefs

Sequence in context: A289311 A351926 A345303 * A029908 A081758 A106492

Adjacent sequences: A345307 A345308 A345309 * A345311 A345312 A345313

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 13 2021

Status

approved