A214662 Greatest prime divisor of 1 + 2^2 + 3^3 + ... + n^n.
5, 2, 3, 3413, 50069, 8089, 487, 2099, 10405071317, 1274641129, 164496735539, 3514531963, 15624709, 23747111, 10343539, 56429700667, 1931869473647715169, 2383792821710269, 144326697012150473, 2053857208873393249, 128801386946535261205906957, 2298815880166789
Offset: 2
Keywords
Examples
a(2) = 5 divides 1 + 2^2 ; a(3) = 2 divides 1 + 2^2 + 3^3 = 32 ; a(4) = 3 divides 1 + 2^2 + 3^3 + 4^4 = 288 = 2^5*3^2 ; a(5) = 3413 divides 1 + 2^2 + 3^3 + 4^4 + 5^5 = 3413. a(13) = 3514531963 divides 1 + 2^2 + 3^3 + ... + 13^13 = 88799 * 3514531963.
Links
- Amiram Eldar, Table of n, a(n) for n = 2..73
Programs
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Magma
[Max(PrimeDivisors(&+[k^k:k in [1..n]])):n in [2..23]]; // Marius A. Burtea, Feb 09 2020
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Maple
with (numtheory): s:= proc(n) option remember; `if`(n=1, 1, s(n-1)+n^n) end: a:= n-> max(factorset(s(n))[]): seq (a(n), n=2..23); # Alois P. Heinz, Jul 24 2012
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Mathematica
s = 1; Table[s = s + n^n; FactorInteger[s][[-1, 1]], {n, 2, 24}] (* T. D. Noe, Jul 25 2012 *) Module[{nn=30,lst},lst=Table[n^n,{n,nn}];Table[FactorInteger[Total[Take[lst,k]]][[-1,1]],{k,2,nn}]] (* Harvey P. Dale, Oct 09 2022 *) -
PARI
a(n) = vecmax(factor(sum(k=1, n, k^k))[,1]); \\ Michel Marcus, Feb 09 2020