A135324 a(n) = Sum_{k=1..phi(n)} k*t(k), where t(k) is the k-th positive integer which is coprime to n and phi(n) is the number of positive integers which are <= n and are coprime to n.

1, 1, 5, 7, 30, 11, 91, 50, 120, 64, 385, 76, 650, 191, 354, 372, 1496, 243, 2109, 468, 1081, 795, 3795, 560, 3450, 1336, 3033, 1432, 7714, 692, 9455, 2856, 4595, 3056, 6974, 1836, 16206, 4299, 7766, 3576, 22140, 2126, 25585, 6100, 8922, 7711, 33511

Offset

1,3

Links

Table of n, a(n) for n=1..47.

Formula

a(n) = Sum_{k=1..A000010(n)} k*A126572(n,k). - R. J. Mathar, Jan 30 2008

Example

The positive integers that are coprime to 12 and are <= 12 are 1,5,7,11. So a(12) = 1*1 + 2*5 + 3*7 + 4*11 = 1+10+21+44 =76.

Maple

A126572 := proc(n, k) local a, i ; a := 1 ; for i from 1 to k do if i = k then RETURN(a) ; fi ; a := a+1 ; while gcd(a, n) <> 1 do a := a+1 ; od; od: end: A135324 := proc(n) add( k*A126572(n, k), k=1..numtheory[phi](n)) ; end: for n from 1 to 80 do printf("%d, ", A135324(n) ) ; od: # R. J. Mathar, Jan 30 2008

Crossrefs

Sequence in context: A153411 A081630 A307532 * A107639 A069688 A158323

Adjacent sequences: A135321 A135322 A135323 * A135325 A135326 A135327

Keyword

nonn

Author

Leroy Quet, Dec 06 2007

Extensions

More terms from R. J. Mathar, Jan 30 2008

Status

approved