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%I #24 May 23 2016 08:32:28
%S 2,1,406,2926,81810,521626,4276350,1590715126,266048146
%N Call n/m a superdivisor of n if n/m + n divides (n/m)^(n/m) + n, (n/m)^n + n/m and n^(n/m) + n/m. This sequence gives the smallest number with n superdivisors.
%e a(0) = 2 because 2/1 + 2 does not divide (2/1)^(2/1) + 2, (2/1)^2 + 2/1, 2^(2/1) + 2/1 and 2/2 + 2 does not divide (2/2)^(2/2) + 2, (2/2)^2 + 2/2, 2^(2/2) + 2/2: 4 does not divide 6, 6, 6 and 3 does not divide 3, 2, 3.
%e a(0) = 2 with superdivisors {}.
%e a(1) = 1 with superdivisor {1}.
%e a(2) = 406 with superdivisors {29, 203}.
%e a(3) = 2926 with superdivisors {77, 209, 1463}.
%e a(4) = 81810 with superdivisors {405, 909, 2727, 13635}.
%e a(5) = 521626 with superdivisors {4921, 7049, 13727, 37259, 260813}.
%e a(6) = 4276350 with superdivisors {2925, 16575, 54825, 237575, 427635, 712725}.
%e a(7) = 1590715126 with superdivisors {607607, 939029, 4253249, 10329319, 61181351, 113622509, 795357563}.
%e a(8) = 266048146 with superdivisors {538559, 655291, 1000181, 1461803, 2714777, 10232621, 19003439, 133024073}.
%o (PARI) superdivisors(n)=select(d->Mod(d, d+n)^d==-n && Mod(d, d+n)^n==-d && Mod(n, d+n)^d==-d, divisors(n))
%o a(n)=my(k); while(#superdivisors(k++)!=n, ); k \\ _Charles R Greathouse IV_, May 06 2016
%Y Cf. A247477, A254748.
%K nonn,more
%O 0,1
%A _Juri-Stepan Gerasimov_, Jan 19 2015
%E a(4)-a(6) from _Charles R Greathouse IV_, Feb 19 2015.
%E Edited by _Charles R Greathouse IV_, May 06 2016
%E a(7)-a(8) from _Charles R Greathouse IV_, May 23 2016
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