The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A364268 a(n) = Sum_{k=1..n} k^2*sigma_2(k), where sigma_2 is A001157. 2
 1, 21, 111, 447, 1097, 2897, 5347, 10787, 18158, 31158, 45920, 76160, 104890, 153890, 212390, 299686, 383496, 530916, 661598, 879998, 1100498, 1395738, 1676108, 2165708, 2572583, 3147183, 3744963, 4568163, 5276285, 6446285, 7370767, 8768527, 10097107 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Table of n, a(n) for n=1..33. Wikipedia, Faulhaber's formula. FORMULA a(n) = Sum_{k=1..n} k^4 * A000330(floor(n/k)). a(n) ~ (zeta(3)/5) * n^5. - Amiram Eldar, Oct 20 2023 MATHEMATICA Accumulate[Table[n^2*DivisorSigma[2, n], {n, 1, 33}]] (* Amiram Eldar, Oct 20 2023 *) PROG (PARI) f(n, m) = (subst(bernpol(m+1, x), x, n+1)-subst(bernpol(m+1, x), x, 0))/(m+1); a(n, s=2, t=2) = sum(k=1, n, k^(s+t)*f(n\k, s)); (Python) def A364268(n): return sum(k**4*(m:=n//k)*(m+1)*((m<<1)+1)//6 for k in range(1, n+1)) # Chai Wah Wu, Oct 20 2023 (Python) from math import isqrt def A364268(n): return (((s:=isqrt(n))*(s+1)*(2*s+1))**2*(1-3*s*(s+1))//6 + sum((q:=n//k)*(q+1)*(2*q+1)*k**2*(5*k**2+3*q*(q+1)-1) for k in range(1, s+1)))//30 # Chai Wah Wu, Oct 21 2023 CROSSREFS Cf. A356125, A364269. Cf. A000330, A001157. Sequence in context: A157886 A039456 A182827 * A255285 A157265 A275916 Adjacent sequences: A364265 A364266 A364267 * A364269 A364270 A364271 KEYWORD nonn,easy AUTHOR Seiichi Manyama, Oct 20 2023 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 19 13:04 EDT 2024. Contains 372692 sequences. (Running on oeis4.)