A345303 a(n) = Sum_{p|n, p prime} p * gcd(p,n/p).

0, 2, 3, 4, 5, 5, 7, 4, 9, 7, 11, 7, 13, 9, 8, 4, 17, 11, 19, 9, 10, 13, 23, 7, 25, 15, 9, 11, 29, 10, 31, 4, 14, 19, 12, 13, 37, 21, 16, 9, 41, 12, 43, 15, 14, 25, 47, 7, 49, 27, 20, 17, 53, 11, 16, 11, 22, 31, 59, 12, 61, 33, 16, 4, 18, 16, 67, 21, 26, 14, 71, 13, 73, 39, 28

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..75.

Example

a(18) = Sum_{p|18} p * gcd(p,18/p) = 2*gcd(2,9) + 3*gcd(3,6) = 2*1 + 3*3 = 11.

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

Cf. A345266.

Sequence in context: A238714 A289311 A351926 * A345310 A029908 A081758

Adjacent sequences: A345300 A345301 A345302 * A345304 A345305 A345306

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 13 2021

Status

approved