A333172 - OEIS

%I #10 Mar 10 2020 06:31:07

%S 1,4,10,28,46,88,126,219,303,429,531,717,897,1221,1419,1761,2019,2559,

%T 2993,3539,3941,4697,5285,6257,6835,7777,8455,9787,10735,12001,12973,

%U 14569,15871,17851,19111,20953,22251,24735,26577,28863,30465,33078,35202,38736

%N a(n) = Sum_{k=0..n} sigma(k^2 + 1), where sigma(k) is the sum of divisors of k (A000203).

%D Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 166.

%H Amiram Eldar, <a href="/A333172/b333172.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ (5*G/Pi^2) * n^3, where G is Catalan's constant (A006752).

%e a(0) = sigma(0^2 + 1) = sigma(1) = 1.

%e a(1) = sigma(0^2 + 1) + sigma(1^2 + 1) = sigma(1) + sigma(2) = 1 + 3 = 4.

%t Accumulate @ Table[DivisorSigma[1, k^2 + 1], {k, 0, 100}]

%o (PARI) a(n) = sum(k=0, n, sigma(k^2+1)); \\ _Michel Marcus_, Mar 10 2020

%Y Partial sums of A193433.

%Y Cf. A000203, A002522, A006752.

%K nonn

%O 0,2

%A _Amiram Eldar_, Mar 09 2020