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A055486
Number of solutions to sigma(x) = n!.
6
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.
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:
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