

A119584


a(n) = Sum_{k=1..phi(n)1} t(n,k)*t(n,k+1), where t(n,k) is the kth 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, 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
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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



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, #v1, v[k]*v[k+1]); \\ Michel Marcus, Mar 07 2024


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



