A127413 a(n) = Sum_{1<=k<=n, gcd(k,n)=1} prime(k).

2, 2, 5, 7, 17, 13, 41, 35, 59, 47, 129, 61, 197, 113, 163, 177, 381, 161, 501, 245, 393, 345, 791, 311, 805, 515, 813, 569, 1371, 409, 1593, 895, 1177, 973, 1519, 793, 2427, 1271, 1753, 1201, 3087, 963, 3447, 1707, 2101, 1989, 4227, 1531, 4091, 2009, 3299

Offset: 1

Author

Gary W. Adamson, Jan 13 2007

Keywords

• nonn
• easy
• look

Examples

			a(9) = 59 since k ranges over {1, 2, 4, 5, 7, 8} and p(1) + p(2) + p(4) + p(5) + p(7) + p(8) = 2 + 3 + 7 + 11 + 17 + 19 = 59.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A054521.

Programs

Maple

a:= n-> add(`if`(igcd(n, k)=1, ithprime(k), 0), k=1..n):
seq(a(n), n=1..60);  # Alois P. Heinz, Oct 23 2009

Formula

M * V where M = A054521 is an infinite lower triangular matrix and V = the sequence of primes (A000040) regarded as a vector.

Extensions

More terms from Alois P. Heinz, Oct 23 2009