A349555 a(n) = Sum_{p<=n, p prime} p^floor(1/gcd(n/p)).

0, 1, 3, 4, 6, 7, 11, 16, 15, 12, 18, 25, 29, 34, 35, 40, 42, 55, 59, 72, 69, 66, 78, 97, 96, 87, 98, 93, 101, 122, 130, 159, 148, 143, 150, 157, 161, 178, 183, 192, 198, 229, 239, 270, 275, 258, 282, 325, 322, 323, 310, 315, 329, 378, 367, 374, 361, 352, 382, 433, 441, 470

Offset: 1

Author

Wesley Ivan Hurt, Nov 21 2021

Keywords

• nonn

Comments

For each prime number p less than or equal to n, add 1 if p|n, otherwise add p (see example).

Examples

			a(9) = 15; The primes less than or equal to 9 are 2, 3, 5, 7 and only 3|9. We then have, respectively, a(9) = 2 + 1 + 5 + 7 = 15.
		

Crossrefs

Cf. A001221, A066911.

Programs

Mathematica

nterms=100;Table[Total[Map[If[Mod[n,#]==0,1,#]&,Prime[Range[PrimePi[n]]]]],{n,nterms}] (* Paolo Xausa, Nov 22 2021 *)

Formula

a(n) = A001221(n) + A066911(n).