A297795 - OEIS

%I #16 Jan 09 2018 04:23:58

%S 1,2,2,34,2,66,2,66,245,66,2,552,2,66,488,1090,2,552,2,2114,488,66,2,

%T 2600,3127,66,488,2114,2,6802,2,2114,488,66,6252,10376,2,66,488,8364,

%U 2,16104,2,2114,6738,66,2,18152,16809,6316,488,2114,2,16104,6252,35728,488

%N a(n) = Sum_{d|n} min(d, n/d)^5.

%H Seiichi Manyama, <a href="/A297795/b297795.txt">Table of n, a(n) for n = 1..10000</a>

%H H. Cohen, <a href="http://gdz.sub.uni-goettingen.de/dms/resolveppn/?PPN=GDZPPN002311860">Sums involving the values at negative integers of L-functions of quadratic characters</a>, Math. Ann. 217 (1975), no. 3, 271-285. MR0382192 (52 #3080)

%F a(n) = - Sum_{k in Z} (k^4-3*n*k^2+n^2)*H(4*n-k^2) where H() is the Hurwitz class number.

%t f[n_] := Block[{d = Divisors@n}, Plus @@ (Min[#, n/#]^5 & /@ d)]; Array[f, 57] (* _Robert G. Wilson v_, Jan 06 2018 *)

%o (PARI) {a(n) = sumdiv(n, d, min(d, n/d)^5)}

%Y Sum_{d|n} min(d, n/d)^k: A117004 (k=1), A297792 (k=2), A297793 (k=3), A297794 (k=4), this sequence (k=5).

%Y Cf. A259825.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Jan 06 2018