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

Author

Leroy Quet, Nov 12 2004

Keywords

• nonn

Comments

Conjecture: this sequence consists completely of integers.

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

Examples

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

References

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

Links

• Eric Weisstein's World of Mathematics, Leudesdorf Theorem
• Eric Weisstein's World of Mathematics, Bauers Identical Congruence

Crossrefs

Cf. A056855, A000010.

Cf. A093600.

Programs

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 *)

Extensions

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