A336892 Numbers that are a divisor of the sum of their divisors to their own powers.

1, 10, 12, 96, 304, 639, 2052, 2060, 2097, 2940, 5586, 9087, 10550, 38988, 42622, 84380, 128030, 199694, 255240, 342411, 346044, 515316, 673233, 721035, 1053700, 1361943, 2149875, 4206049, 5739687, 6979316, 10896431, 15904273, 138156772, 144608991, 276866005

Offset: 1

Author

Scott R. Shannon, Aug 07 2020

Keywords

• nonn

Comments

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.

Integers k such that k divides A062796(k). - Michel Marcus, Aug 07 2020

a(36) > 280 million if it exists. - David A. Corneth, Aug 10 2020

Examples

			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.
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.
		

Crossrefs

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

Programs

Mathematica

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

PARI

isokb(k) = ! sumdiv(k, d, if (dMichel Marcus, Aug 10 2020

Extensions

a(19)-a(25) from Amiram Eldar, Aug 08 2020

a(26)-a(32) from Michel Marcus, Aug 10 2020

a(33)-a(35) from David A. Corneth, Aug 10 2020