A175346 a(n) = Sum_{k=1..n^2} d(k), d(k) = number of divisors of k (A000005).

1, 8, 23, 50, 87, 140, 201, 280, 373, 482, 605, 746, 897, 1070, 1261, 1466, 1689, 1932, 2189, 2468, 2761, 3074, 3405, 3764, 4127, 4518, 4925, 5360, 5807, 6276, 6757, 7262, 7789, 8342, 8915, 9502, 10107

Offset

1,2

Comments

Generalized sequence: Sum_{k=1..T(n)} d(k). In this sequence T(n)=n^2, in A085831 T(n)=2^n, in A006218 T(n)=n. Other examples not in the OEIS: T(n)=p(n) n-th prime, T(n)=n*(n+1)/2 n-th triangular number, T(n)= F(n) n-th Fibonacci number, etc.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) ~ 2n^2 log n. [Charles R Greathouse IV, Aug 21 2011]

a(n) = n^2 + 2*Sum_{k=2..n} floor(n^2/k). - Chai Wah Wu, Oct 24 2023

Mathematica

Table[Sum[DivisorSigma[0, k], {k, 1, n^2}], {n, 1, 80}] (* Carl Najafi, Aug 21 2011 *)

Prog

(PARI) a(n)=sum(k=1, n^2, numdiv(k)) \\ Charles R Greathouse IV, Aug 21 2011
(Python)
def A175346(n): return (m:=n**2)+(sum(m//k for k in range(2, n+1))<<1) # Chai Wah Wu, Oct 24 2023

Crossrefs

Cf. A085831, A000005, A006218.

Sequence in context: A033951 A209992 A212118 * A225280 A218711 A270694

Adjacent sequences: A175343 A175344 A175345 * A175347 A175348 A175349

Keyword

nonn

Author

Ctibor O. Zizka, Apr 17 2010

Extensions

More terms from Carl Najafi, Aug 21 2011

Status

approved