A297793 a(n) = Sum_{d|n} min(d, n/d)^3.

1, 2, 2, 10, 2, 18, 2, 18, 29, 18, 2, 72, 2, 18, 56, 82, 2, 72, 2, 146, 56, 18, 2, 200, 127, 18, 56, 146, 2, 322, 2, 146, 56, 18, 252, 416, 2, 18, 56, 396, 2, 504, 2, 146, 306, 18, 2, 632, 345, 268, 56, 146, 2, 504, 252, 832, 56, 18, 2, 882, 2, 18, 742, 658, 252

Offset: 1

Author

Seiichi Manyama, Jan 06 2018

Keywords

• nonn

Links

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

Crossrefs

Sum_{d|n} min(d, n/d)^k: A117004 (k=1), A297792 (k=2), this sequence (k=3), A297794 (k=4), A297795 (k=5).

Cf. A259825.

Programs

Mathematica

a[n_] := DivisorSum[n, Min[#, n/#]^3 &]; Array[a, 65] (* Amiram Eldar, Oct 04 2023*)

PARI

{a(n) = sumdiv(n, d, min(d, n/d)^3)}

Formula

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