A344457 a(n) = Sum_{d|n} d * Omega(d).

0, 2, 3, 10, 5, 17, 7, 34, 21, 27, 11, 61, 13, 37, 38, 98, 17, 89, 19, 95, 52, 57, 23, 181, 55, 67, 102, 129, 29, 162, 31, 258, 80, 87, 82, 277, 37, 97, 94, 279, 41, 220, 43, 197, 191, 117, 47, 485, 105, 227, 122, 231, 53, 386, 126, 377, 136, 147, 59, 506, 61, 157, 259, 642

Offset

1,2

Comments

If p is prime, a(p) = Sum_{d|p} d * Omega(d) = 1*0 + p*1 = p.

Links

Table of n, a(n) for n=1..64.

Example

a(6) = Sum_{d|6} d * Omega(d) = 1*0 + 2*1 + 3*1 + 6*2 = 17.

Mathematica

Table[Sum[k*PrimeOmega[k] (1 - Ceiling[n/k] + Floor[n/k]), {k, n}], {n, 100}]

Crossrefs

Cf. A001222 (Omega).

Sequence in context: A347271 A266552 A263716 * A175899 A328613 A064946

Adjacent sequences: A344454 A344455 A344456 * A344458 A344459 A344460

Keyword

nonn

Author

Wesley Ivan Hurt, May 19 2021

Status

approved