A175232 The smallest prime divisor of 1 + 2^2 + 3^3 + ... + n^n.

5, 2, 2, 3413, 50069, 2, 2, 7, 10405071317, 2, 2, 88799, 3, 2, 2, 3, 3, 2, 2, 5, 3, 2, 2, 3, 7, 2, 2, 7, 208492413443704093346554910065262730566475781, 2, 2, 3, 17, 2, 2, 5, 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

Offset: 2

Author

Michel Lagneau, Mar 09 2010

Keywords

• nonn

Examples

			a(2) = 5 divides 1 + 2^2.
a(3) = 2 divides 1 + 2^2 + 3^3 = 32.
a(4) = 2 divides 1 + 2^2 + 3^3 + 4^4 = 288.
a(5) = 3413 divides 1 + 2^2 + 3^3 + 4^4 + 5^5 = 3413.
a(13) = 88799 divides 1 + 2^2 + 3^3 + ... + 13^13 = 88799 * 3514531963.
		

Crossrefs

Cf. A073826, A122166.

Programs

Maple

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:

Mathematica

a[n_] := FactorInteger[Sum[k^k, {k, 1, n}]][[1, 1]]; Array[a, 20, 2] (* Amiram Eldar, Feb 04 2020 *)

Formula

a(n) = A020639(A001923(n)).

Extensions

Edited by R. J. Mathar, Mar 16 2010

a(61)-a(65) from Amiram Eldar, Feb 04 2020