A331071 a(n) = Sum_{k <= n} r_2(k)^2*d(k+1), where r_2 = A004018, d = A000005.
1, 33, 65, 65, 97, 353, 353, 353, 401, 465, 593, 593, 593, 849, 849, 849, 881, 1265, 1297, 1297, 1553, 1553, 1553, 1553, 1553, 2129, 2385, 2385, 2385, 2897, 2897, 2897, 2961, 2961, 3217, 3217, 3249, 3505, 3505, 3505, 3633, 4145, 4145, 4145, 4145, 4401, 4401, 4401, 4401, 4497, 5073, 5073, 5201, 5713, 5713
Offset: 0
Keywords
References
- Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 163.
Links
- Amiram Eldar, Table of n, a(n) for n = 0..10000
- Karl-Heinz Indlekofer, Eine asymptotische Formel in der Zahlentheorie, (German) Arch. Math. (Basel) 23 (1972), 619-624. MR0318080 (47 #6629).
Programs
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Mathematica
Accumulate @ Table[SquaresR[2, n]^2 * DivisorSigma[0, n+1], {n, 0, 50}] (* Amiram Eldar, Mar 05 2020 *)
Formula
a(n) ~ c * n * log(n)^2, where c is a constant. - Amiram Eldar, Mar 05 2020
Comments