A331132 a(n) = Sum_{i=1..n} d(i)^2*d(i+1), where d(n) = A000005(n).

2, 10, 22, 40, 56, 88, 104, 152, 188, 220, 244, 316, 332, 396, 476, 526, 550, 622, 646, 790, 854, 886, 918, 1110, 1146, 1210, 1306, 1378, 1410, 1538, 1562, 1706, 1770, 1834, 1978, 2140, 2156, 2220, 2348, 2476, 2508, 2636, 2660, 2876, 3020, 3052, 3092, 3392, 3446, 3590, 3686, 3758, 3790, 4046, 4174, 4430

Offset

1,1

References

Steven R. Finch, Mathematical Constants II, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 2018, p. 162.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..5000

Yoichi Motohashi, An asymptotic formula in the theory of numbers, Acta Arith. 16 (1969/70), 255-264. MR0266884 (42 #1786).

J. Sandor, D. S. Mitrinovic, B. Crstici, Handbook of Number Theory I, Volume 1, Springer, 2005, p. 63.

Formula

a(n) ~ (c/Pi^2) * n * log(n)^4, where c = Product_{p prime} (1 - 1/p + (1/p)*(1 - 1/p)^2*(1 + 1/p)^(-1)) = 0.358231... - Amiram Eldar, Mar 08 2020

Mathematica

Accumulate[a[n_]:=DivisorSum[n+1, DivisorSigma[0, n]^2 &]; Array[a, 56]] (* Vincenzo Librandi, Jan 12 2020 *)

Prog

(Magma) [&+[#Divisors(i)^2*#Divisors(i+1):i in [1..n]]:n in [1..60]]; // Marius A. Burtea, Jan 12 2020

Crossrefs

Cf. A000005, A331133.

Sequence in context: A225290 A065450 A090288 * A032526 A294538 A096183

Adjacent sequences: A331129 A331130 A331131 * A331133 A331134 A331135

Keyword

nonn

Author

N. J. A. Sloane, Jan 11 2020

Status

approved