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%I #30 Jul 19 2016 16:19:59
%S 1,0,1,3,4,15,33,111,382,1195,3366,14077,53265,229603,910254,4524029,
%T 18879944,91336498,561832582,2801857644,14652294729,78894985156,
%U 408373652461,2378940665083,11939275822636,71931330299023,392274481206066,2626331088771946
%N Number of solutions to sigma(x) = n!.
%D R. K. Guy (1981): Unsolved Problems In Number Theory, B39.
%H Max A. Alekseyev, <a href="https://www.emis.de/journals/JIS/VOL19/Alekseyev/alek5.html">Computing the Inverses, their Power Sums, and Extrema for Euler's Totient and Other Multiplicative Functions</a>. Journal of Integer Sequences, Vol. 19 (2016), Article 16.5.2
%F a(n) = A054973(n!) = Cardinality[{x; A000203(x) = A000142(n)}].
%e For n = 9, solutions to sigma(x) = n! = 362880 form a set {97440, ..., 361657} of size 382, so a(9) = 382.
%p 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:
%Y Cf. A000142, A000203, A054973, A014197, A055488, A055489, A055506.
%K nonn
%O 1,4
%A _Labos Elemer_, Jun 28 2000
%E More terms from _Jud McCranie_, Oct 09 2000
%E a(13)-a(14) from _Donovan Johnson_, Nov 22 2008
%E a(15) from _Ray Chandler_, Jan 13 2009
%E a(16)-a(28) from _Max Alekseyev_, Jan 23 2012
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