%I A031971
%S A031971 1,5,36,354,4425,67171,1200304,24684612,574304985,14914341925,
%T A031971 427675990236,13421957361110,457593884876401,16841089312342855,
%U A031971 665478473553144000,28101527071305611528,1262899292504270591313
%N A031971 Sum k^n, k=1..n.
%C A031971 p^(3k-1) divides a(p^k) for prime p>2 and k=1,2,3,4.. or p^2 divides 
               a(p) for prime p>2. p^5 divides a(p^2) for prime p>2. p^8 divides 
               a(p^3) for prime p>2. p^11 divides a(p^4) for prime p>2. .. p^2 divides 
               a(2p) for prime p>3. p^3 divides a(3p) for prime p>2. p^2 divides 
               a(4p) for prime p>5. p^3 divides a(5p) for prime p>3. p^2 divides 
               a(6p) for prime p>7. .. p divides a(2p-1) for all prime p. p^3 divides 
               a(2p^2-1) for all prime p. p^5 divides a(2p^3-1) for all prime p. 
               .. p divides a((p-1)/2) for p=5,13,17,29,37,41,53,61..=A002144 Pythagorean 
               primes: primes of form 4n+1. - Alexander Adamchuk (alex(AT)kolmogorov.com), 
               Jul 21 2006
%F A031971 a(n) is asymptotic to (e/(e-1))*n^n - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               Dec 17 2003
%F A031971 a(n) = Zeta[ -n] - Zeta[ -n,n+1]. - Alexander Adamchuk (alex(AT)kolmogorov.com), 
               Jul 21 2006
%p A031971 f := n->sum('i'^n,'i'=1..n);
%p A031971 a:=n->sum(mul(k-1, j=2..n), k=2..n): seq(a(n), n=2..18); - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Jun 03 2007
%t A031971 Zeta[ -n] - Zeta[ -n,n+1] - Alexander Adamchuk (alex(AT)kolmogorov.com), 
               Jul 21 2006
%Y A031971 A diagonal of array A103438.
%Y A031971 Cf. A002144.
%Y A031971 Sequence in context: A008785 A081918 A062024 this_sequence A132686 A118018 
               A156355
%Y A031971 Adjacent sequences: A031968 A031969 A031970 this_sequence A031972 A031973 
               A031974
%K A031971 nonn,nice,easy
%O A031971 1,2
%A A031971 Chris du Feu (chris(AT)beckingham0.demon.co.uk)