A055486 Number of solutions to sigma(x) = n!.

1, 0, 1, 3, 4, 15, 33, 111, 382, 1195, 3366, 14077, 53265, 229603, 910254, 4524029, 18879944, 91336498, 561832582, 2801857644, 14652294729, 78894985156, 408373652461, 2378940665083, 11939275822636, 71931330299023, 392274481206066, 2626331088771946

Offset: 1

Author

Labos Elemer, Jun 28 2000

Keywords

• nonn

Examples

			For n = 9, solutions to sigma(x) = n! = 362880 form a set {97440, ..., 361657} of size 382, so a(9) = 382.
		

References

• R. K. Guy (1981): Unsolved Problems In Number Theory, B39.

Links

• Max A. Alekseyev, Computing the Inverses, their Power Sums, and Extrema for Euler's Totient and Other Multiplicative Functions. Journal of Integer Sequences, Vol. 19 (2016), Article 16.5.2

Crossrefs

Cf. A000142, A000203, A054973, A014197, A055488, A055489, A055506.

Programs

Maple

with(numtheory): for f from 1 to 9 do fac := f!: k := 0:for n from 1 to fac do if sigma(n)=fac then k := k+1: fi: od: print( k); od:

Formula

a(n) = A054973(n!) = Cardinality[{x; A000203(x) = A000142(n)}].

Extensions

More terms from Jud McCranie, Oct 09 2000

a(13)-a(14) from Donovan Johnson, Nov 22 2008

a(15) from Ray Chandler, Jan 13 2009

a(16)-a(28) from Max Alekseyev, Jan 23 2012