A119584 a(n) = Sum_{k=1..phi(n)-1} t(n,k)*t(n,k+1), where t(n,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.

0, 0, 2, 3, 20, 5, 70, 53, 121, 87, 330, 117, 572, 305, 507, 553, 1360, 481, 1938, 873, 1586, 1405, 3542, 1241, 3846, 2415, 4006, 2765, 7308, 1875, 8990, 4945, 6828, 5675, 9333, 4525, 15540, 8053, 11567, 7745, 21320, 6047, 24682, 12005, 15244, 14625

Offset

1,3

Comments

All primes are records and there exists records which are not primes, but they are rare (see A120033). - Robert G. Wilson v, Jun 05 2006

Links

Table of n, a(n) for n=1..46.

Example

The positive integers which are <= 8 and are coprime to 8 are 1, 3, 5 and 7. So a(8) = 1*3 + 3*5 + 5*7 = 53.

Mathematica

a[n_] := Block[{s = Select[ Range@n, GCD[ #, n] == 1 &]}, Plus @@ (Most@s*Rest@s)]; Array[a, 46] (* Robert G. Wilson v, Jun 05 2006 *)

Prog

(PARI) a(n) = my(v=select(x->gcd(x, n)==1, [1..n])); sum(k=1, #v-1, v[k]*v[k+1]); \\ Michel Marcus, Mar 07 2024

Crossrefs

Sequence in context: A038584 A108022 A108884 * A376015 A344546 A279719

Adjacent sequences: A119581 A119582 A119583 * A119585 A119586 A119587

Keyword

nonn

Author

Leroy Quet, May 31 2006

Extensions

More terms from Robert G. Wilson v, Jun 05 2006

Status

approved