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

Author

Leroy Quet, Dec 06 2007

Keywords

• nonn

Examples

			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.
		

Programs

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

Formula

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

Extensions

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