A109607 Sum of coprimes of n greater than 1.

0, 0, 0, 2, 3, 9, 5, 20, 15, 26, 19, 54, 23, 77, 41, 59, 63, 135, 53, 170, 79, 125, 109, 252, 95, 249, 155, 242, 167, 405, 119, 464, 255, 329, 271, 419, 215, 665, 341, 467, 319, 819, 251, 902, 439, 539, 505, 1080, 383, 1028, 499, 815, 623, 1377, 485, 1099, 671, 1025

Offset

0,4

Links

Robert P. P. McKone, Table of n, a(n) for n = 0..14143

Formula

a(n) = A023896(n) - 1. - Joerg Arndt, Mar 08 2013

G.f.: -x/(1 - x) + Sum_{k>=1} mu(k)*k*x^k/(1 - x^k)^3. - Ilya Gutkovskiy, May 28 2019

Example

a(9) = 26 because 2,4,5,7,8 are coprime to 9 and 2+4+5+7+8 = 26.

Mathematica

a[n_] := Total@Select[Range[2, n], CoprimeQ[n, #] &]; Table[a[n], {n, 0, 57}] (* Robert P. P. McKone, Nov 12 2023 *)

Prog

(PARI) a(n) = sum(i=2, n-1, i*(gcd(i, n)==1)); \\ Michel Marcus, Mar 08 2013
(PARI) a(n)=if(n<3, 0, n*eulerphi(n)/2-1) \\ Charles R Greathouse IV, Mar 08 2013

Crossrefs

Cf. A023896.

Sequence in context: A120725 A253046 A324576 * A324581 A127612 A038756

Adjacent sequences: A109604 A109605 A109606 * A109608 A109609 A109610

Keyword

nonn,look

Author

Andrew Weimholt, Jul 31 2005

Extensions

Added "greater than 1" to name to match terms, Joerg Arndt, Mar 08 2013

Status

approved