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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 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 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

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Last modified February 1 07:16 EST 2023. Contains 359981 sequences. (Running on oeis4.)