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

1,2

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

Links

Table of n, a(n) for n=1..35.

Example

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.

Mathematica

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

Prog

(PARI) isokb(k) = ! sumdiv(k, d, if (d<k, Mod(d, k)^d)); \\ Michel Marcus, Aug 10 2020

Crossrefs

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

Sequence in context: A333258 A370976 A241252 * A301905 A167321 A258484

Adjacent sequences: A336889 A336890 A336891 * A336893 A336894 A336895

Keyword

nonn

Author

Scott R. Shannon, Aug 07 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

Status

approved