A375790 - OEIS

%I #7 Sep 20 2024 06:39:32

%S 1,9,10,112,136,514,528,625,652,1072,1152,1216,1984,2016,2956,3808,

%T 4320,4672,5056,6592,8716,9801,10432,13552,29632,32896,38476,40096,

%U 47296,72256,117649,148960,174592,181000,232128,245025,246208,288832,289216,355492,392448,405952,419392,458752,499968

%N Numbers k such that (sigma(k) - k)^(sigma(k) - k) == k (mod sigma(k)), where sigma = A000203.

%e 9 is in this sequence because (sigma(9)-9)^(sigma(9)-9) = (13-4)^(13-4) = 256 modulo 13 equal to 9.

%o (Magma) [k: k in [1..50000] | (SumOfDivisorse(k)-k)^(SumOfDivisorse(k)-k) mod SumOfDivisors(k) eq k];

%o (PARI) isok(k) = my(s=sigma(k)); Mod(s-k, s)^(s-k) == k \\ _Michel Marcus_, Aug 29 2024

%Y Cf. A000203, A001065, A036878, A375488.

%K nonn

%O 1,2

%A _Juri-Stepan Gerasimov_, Aug 29 2024

%E More terms from _Michel Marcus_, Aug 29 2024