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A055489 Largest number x such that sum of divisors of x is n!.

%I A055489 #28 May 17 2022 06:27:08
%S A055489 5,23,95,719,5039,39917,361657,3624941,39904153,479001599,6226862869,
%T A055489 87178291199,1307672080867,20922780738961,355687390376431,
%U A055489 6402373545694717,121645099711277873,2432902005056589697,51090942157413850441
%N A055489 Largest number x such that sum of divisors of x is n!.
%C A055489 For n = 1, a(1) = 1; for n = 2 there is no solution.
%C A055489 For n in A002982, a(n) = n!-1.
%D A055489 R. K. Guy (1981): Unsolved Problems In Number Theory, B39.
%H A055489 Ray Chandler, <a href="/A055489/b055489.txt">Table of n, a(n) for n=3..52</a>
%H A055489 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 A055489 a(n) = Max{x; Sigma[x] = n!} = Max{x; A000203(x) = A000142(n)}
%F A055489 a(n) = A057637(A000142(n)). - _Ray Chandler_, Jan 15 2009
%F A055489 a(A002982(n)) = A000142(A002982(n)) - 1. - _Ray Chandler_, Jan 15 2009
%e A055489 For n = 6, the 15 solutions are as follows: {264, 270, 280, 354, 376, 406, 418, 435, 459, 478, 537, 623, 649, 667, 719}.
%o A055489 (PARI) a(n) = {fn = n!; x = fn - 1; while(sigma(x) != fn, x--); x;} \\ _Michel Marcus_, Dec 17 2013
%Y A055489 Cf. A000203, A000142, A002982, A055486, A055488, A057637.
%K A055489 nonn
%O A055489 3,1
%A A055489 _Labos Elemer_, Jun 28 2000
%E A055489 More terms from _Jud McCranie_, Oct 09 2000
%E A055489 a(15) from _Donovan Johnson_, Aug 31 2008
%E A055489 a(16)-a(19) from _Donovan Johnson_, Nov 22 2008
%E A055489 a(20)-a(52) from _Ray Chandler_, Jan 15 2009