A345305 a(n) = n * Sum_{p|n, p prime} gcd(p,n/p) / p.

0, 1, 1, 4, 1, 5, 1, 8, 9, 7, 1, 16, 1, 9, 8, 16, 1, 27, 1, 24, 10, 13, 1, 32, 25, 15, 27, 32, 1, 31, 1, 32, 14, 19, 12, 72, 1, 21, 16, 48, 1, 41, 1, 48, 54, 25, 1, 64, 49, 75, 20, 56, 1, 81, 16, 64, 22, 31, 1, 92, 1, 33, 72, 64, 18, 61, 1, 72, 26, 59, 1, 144, 1, 39, 100, 80, 18

Offset

1,4

Comments

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

Links

Table of n, a(n) for n=1..77.

Example

a(18) = 18 * Sum_{p|18} gcd(p,18/p) / p = 18 * (gcd(2,9)/2 + gcd(3,6)/3) = 18 * (1/2 + 1) = 27.

Mathematica

Table[n*Sum[(1/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: A157104 A101322 A029644 * A024919 A328385 A328099

Adjacent sequences: A345302 A345303 A345304 * A345306 A345307 A345308

Keyword

nonn

Author

Wesley Ivan Hurt, Jun 13 2021

Status

approved