A099940 a(n) = 2*(A056855(n)) /(phi(n)*n), where phi() is the Euler phi function.

2, 1, 1, 1, 5, 1, 84, 11, 184, 15, 193248, 23, 19056960, 833, 33740, 64035, 520105017600, 2473, 130859579289600, 203685, 963513600, 23748417, 16397141420298240000, 645119, 555804546402631680, 8527366575

Offset

1,1

Comments

Conjecture: this sequence consists completely of integers.

From Leudesdorf's theorem this is an integer sequence. - Benoit Cloitre, Nov 13 2004

References

G. H. Hardy and E. M. Wright, Introduction to the theory of numbers, fifth edition, Oxford Science Publication, pp. 100-102

Links

Table of n, a(n) for n=1..26.

Eric Weisstein's World of Mathematics, Leudesdorf Theorem

Eric Weisstein's World of Mathematics, Bauers Identical Congruence

Example

a(6) = 2*(1 + 1/5)*1*5/(6*2) = 1.

Mathematica

f[n_] := Block[{k = Select[Range[n], GCD[ #, n] == 1 &]}, 2Plus @@ (Times @@ k*Plus @@ 1/k)/EulerPhi[n]/n]; Table[ f[n], {n, 26}] (* Robert G. Wilson v, Nov 16 2004 *)

Crossrefs

Cf. A056855, A000010.

Cf. A093600.

Sequence in context: A082063 A260148 A327778 * A157249 A351861 A343233

Adjacent sequences: A099937 A099938 A099939 * A099941 A099942 A099943

Keyword

nonn

Author

Leroy Quet, Nov 12 2004

Extensions

More terms from Don Reble, Nov 12 2004, who remarks that the conjecture is true for n <= 5000.

Status

approved