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%I #7 Feb 04 2020 03:57:58
%S 5,2,2,3413,50069,2,2,7,10405071317,2,2,88799,3,2,2,3,3,2,2,5,3,2,2,3,
%T 7,2,2,7,208492413443704093346554910065262730566475781,2,2,3,17,2,2,5,
%U 61,2,2,71,11,2,2,11,7,2,2,5,3,2,2,3,3,2,2,23,3,2,2,3,44818693,2,2,5
%N The smallest prime divisor of 1 + 2^2 + 3^3 + ... + n^n.
%F a(n) = A020639(A001923(n)).
%e a(2) = 5 divides 1 + 2^2.
%e a(3) = 2 divides 1 + 2^2 + 3^3 = 32.
%e a(4) = 2 divides 1 + 2^2 + 3^3 + 4^4 = 288.
%e a(5) = 3413 divides 1 + 2^2 + 3^3 + 4^4 + 5^5 = 3413.
%e a(13) = 88799 divides 1 + 2^2 + 3^3 + ... + 13^13 = 88799 * 3514531963.
%p with(numtheory): s :=1: for n from 2 to 60 do ;s := s+ n^n: s1 := ifactors(s)[2] : s2 :=s1[i][1], i=1..nops(s1):print(s1[1][1]):od:
%t a[n_] := FactorInteger[Sum[k^k, {k, 1, n}]][[1, 1]]; Array[a, 20, 2] (* _Amiram Eldar_, Feb 04 2020 *)
%Y Cf. A073826, A122166.
%K nonn
%O 2,1
%A _Michel Lagneau_, Mar 09 2010
%E Edited by _R. J. Mathar_, Mar 16 2010
%E a(61)-a(65) from _Amiram Eldar_, Feb 04 2020