cp's OEIS Frontend

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

%I A175346 #26 Oct 25 2023 09:30:25
%S A175346 1,8,23,50,87,140,201,280,373,482,605,746,897,1070,1261,1466,1689,
%T A175346 1932,2189,2468,2761,3074,3405,3764,4127,4518,4925,5360,5807,6276,
%U A175346 6757,7262,7789,8342,8915,9502,10107
%N A175346 a(n) = Sum_{k=1..n^2} d(k), d(k) = number of divisors of k (A000005).
%C A175346 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.
%H A175346 Amiram Eldar, <a href="/A175346/b175346.txt">Table of n, a(n) for n = 1..10000</a>
%F A175346 a(n) ~ 2n^2 log n. [_Charles R Greathouse IV_, Aug 21 2011]
%F A175346 a(n) = n^2 + 2*Sum_{k=2..n} floor(n^2/k). - _Chai Wah Wu_, Oct 24 2023
%t A175346 Table[Sum[DivisorSigma[0, k], {k, 1, n^2}], {n, 1, 80}] (* _Carl Najafi_, Aug 21 2011 *)
%o A175346 (PARI) a(n)=sum(k=1,n^2,numdiv(k)) \\ _Charles R Greathouse IV_, Aug 21 2011
%o A175346 (Python)
%o A175346 def A175346(n): return (m:=n**2)+(sum(m//k for k in range(2,n+1))<<1) # _Chai Wah Wu_, Oct 24 2023
%Y A175346 Cf. A085831, A000005, A006218.
%K A175346 nonn
%O A175346 1,2
%A A175346 _Ctibor O. Zizka_, Apr 17 2010
%E A175346 More terms from _Carl Najafi_, Aug 21 2011