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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
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
Sequence in context: A157886 A039456 A182827 * A255285 A157265 A275916
KEYWORD
nonn,easy
AUTHOR
Seiichi Manyama, Oct 20 2023
STATUS
approved

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