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A214662 Greatest prime divisor of 1 + 2^2 + 3^3 + ... + n^n. 1
5, 2, 3, 3413, 50069, 8089, 487, 2099, 10405071317, 1274641129, 164496735539, 3514531963, 15624709, 23747111, 10343539, 56429700667, 1931869473647715169, 2383792821710269, 144326697012150473, 2053857208873393249, 128801386946535261205906957, 2298815880166789 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

LINKS

Amiram Eldar, Table of n, a(n) for n = 2..73

FORMULA

a(n) = A006530(A001923(n)).

EXAMPLE

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.

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

MATHEMATICA

s = 1; Table[s = s + n^n; FactorInteger[s][[-1, 1]], {n, 2, 24}] (* T. D. Noe, Jul 25 2012 *)

PROG

(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

CROSSREFS

Cf. A001923, A006530, A073826, A122166, A175232.

Sequence in context: A291690 A073943 A193797 * A277581 A307381 A256167

Adjacent sequences:  A214659 A214660 A214661 * A214663 A214664 A214665

KEYWORD

nonn

AUTHOR

Michel Lagneau, Jul 24 2012

STATUS

approved

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Last modified April 23 01:55 EDT 2021. Contains 343198 sequences. (Running on oeis4.)