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A214662
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Greatest prime divisor of 1 + 2^2 + 3^3 + ... + n^n.
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1
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5, 2, 3, 3413, 50069, 8089, 487, 2099, 10405071317, 1274641129, 164496735539, 3514531963, 15624709, 23747111, 10343539, 56429700667, 1931869473647715169, 2383792821710269, 144326697012150473, 2053857208873393249, 128801386946535261205906957, 2298815880166789
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OFFSET
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2,1
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LINKS
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FORMULA
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EXAMPLE
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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.
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MAPLE
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with (numtheory):
s:= proc(n) option remember; `if`(n=1, 1, s(n-1)+n^n) end:
a:= n-> max(factorset(s(n))[]):
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MATHEMATICA
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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 *)
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PROG
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(PARI) a(n) = vecmax(factor(sum(k=1, n, k^k))[, 1]); \\ Michel Marcus, Feb 09 2020
(Magma) [Max(PrimeDivisors(&+[k^k:k in [1..n]])):n in [2..23]]; // Marius A. Burtea, Feb 09 2020
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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