A336892 - OEIS

%I #33 Aug 14 2020 23:57:03

%S 1,10,12,96,304,639,2052,2060,2097,2940,5586,9087,10550,38988,42622,

%T 84380,128030,199694,255240,342411,346044,515316,673233,721035,

%U 1053700,1361943,2149875,4206049,5739687,6979316,10896431,15904273,138156772,144608991,276866005

%N Numbers that are a divisor of the sum of their divisors to their own powers.

%C As n is a divisor of n^n this sequence is also the numbers that are a divisor of the sum of their proper divisors to their own powers.

%C Integers k such that k divides A062796(k). - _Michel Marcus_, Aug 07 2020

%C a(36) > 280 million if it exists. - _David A. Corneth_, Aug 10 2020

%e 10 is a term as the divisors of 10 are 1,2,5,10 and 1^1+2^2+5^5+10^10 = 3130 + 10^10 which is divisible by 10.

%e 12 is a term as the divisors of 12 are 1,2,3,4,6,12 and 1^1+2^2+3^3+4^4+6^6+12^12 = 46944 + 12^12 which is divisible by 12.

%t seqQ[n_] := Divisible[DivisorSum[n, PowerMod[#, #, n] &], n]; Select[Range[10^5], seqQ] (* _Amiram Eldar_, Aug 10 2020 *)

%o (PARI) isokb(k) = ! sumdiv(k, d, if (d<k, Mod(d, k)^d)); \\ _Michel Marcus_, Aug 10 2020

%Y Cf. A032741, A000005, A001065, A032742, A062796.

%K nonn

%O 1,2

%A _Scott R. Shannon_, Aug 07 2020

%E a(19)-a(25) from _Amiram Eldar_, Aug 08 2020

%E a(26)-a(32) from _Michel Marcus_, Aug 10 2020

%E a(33)-a(35) from _David A. Corneth_, Aug 10 2020