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

1,4

References

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

Links

Table of n, a(n) for n=1..28.

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

Formula

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

Example

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

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:

Crossrefs

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

Sequence in context: A135100 A205485 A344261 * A041665 A052133 A332051

Adjacent sequences: A055483 A055484 A055485 * A055487 A055488 A055489

Keyword

nonn

Author

Labos Elemer, Jun 28 2000

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

Status

approved