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%I #18 Sep 08 2022 08:46:20
%S 0,8,17,1978,73,0,1570497,1009588832,7390478182,1391503283200,
%T 166394893969,151448237549551616,762517292682713,18685202394240778240,
%U 814227337406354049,187036938412352867328077,947615093635545799201,2095989269871299377743863001
%N a(n) = n^sigma(n) mod sigma(n)^n.
%C sigma(n) = the sum of the divisors of n (A000203).
%C n^sigma(n) > sigma(n)^n for all n > 2.
%F a(n) = A100879(n) mod A217872(n).
%F a(n) = 0 for numbers n in A300906.
%F If n is a k-perfect number from A007691, then a(n) = 0 iff k divides n.
%e For n = 6; a(6) = 0 because 6^sigma(6) mod sigma(6)^6 = 6^12 mod 12^6 = 2176782336 mod 2985984 = 0.
%p with(numtheory): seq(n &^ sigma(n) mod sigma(n)^n,n=1..20); # _Muniru A Asiru_, Mar 20 2018
%t Array[With[{s = DivisorSigma[1, #]}, PowerMod[#, s, s^#]] &, 18] (* _Michael De Vlieger_, Mar 16 2018 *)
%o (Magma) [n^SumOfDivisors(n) mod SumOfDivisors(n)^n: n in[1..20]]
%o (PARI) a(n) = my(s=sigma(n)); lift(Mod(n, s^n)^s); \\ _Michel Marcus_, Mar 17 2018
%o (GAP) List([1..20],n->PowerModInt(n,Sigma(n),Sigma(n)^n))); # _Muniru A Asiru_, Mar 20 2018
%Y Cf. A000203, A007691, A100879, A217872, A300906.
%K nonn
%O 1,2
%A _Jaroslav Krizek_, Mar 14 2018