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A331132
a(n) = Sum_{i=1..n} d(i)^2*d(i+1), where d(n) = A000005(n).
2
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
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
Sequence in context: A225290 A065450 A090288 * A032526 A294538 A096183
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jan 11 2020
STATUS
approved