A297795 a(n) = Sum_{d|n} min(d, n/d)^5.

1, 2, 2, 34, 2, 66, 2, 66, 245, 66, 2, 552, 2, 66, 488, 1090, 2, 552, 2, 2114, 488, 66, 2, 2600, 3127, 66, 488, 2114, 2, 6802, 2, 2114, 488, 66, 6252, 10376, 2, 66, 488, 8364, 2, 16104, 2, 2114, 6738, 66, 2, 18152, 16809, 6316, 488, 2114, 2, 16104, 6252, 35728, 488

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

H. Cohen, Sums involving the values at negative integers of L-functions of quadratic characters, Math. Ann. 217 (1975), no. 3, 271-285. MR0382192 (52 #3080)

Formula

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.

Mathematica

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

Prog

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

Crossrefs

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

Cf. A259825.

Sequence in context: A121788 A018976 A074127 * A024176 A349033 A334470

Adjacent sequences: A297792 A297793 A297794 * A297796 A297797 A297798

Keyword

nonn

Author

Seiichi Manyama, Jan 06 2018

Status

approved