A230292 a(n) = Sum_{i=1..n} d(24*i+9) - Sum_{i=1..n} d(6*i+3), where d(n) = A000005(n).

1, 1, 2, 6, 6, 8, 6, 6, 11, 9, 13, 15, 14, 18, 20, 18, 14, 19, 21, 21, 25, 21, 25, 31, 33, 33, 31, 29, 33, 36, 32, 32, 34, 40, 40, 42, 41, 37, 49, 51, 51, 49, 47, 51, 52, 54, 50, 54, 54, 58, 60, 52, 56, 64, 62, 66, 68, 64, 68, 74, 72, 68, 73, 75, 75, 75, 77, 77, 85, 83, 79, 77, 72, 84, 88, 88, 84, 92, 94, 90, 98, 90

Offset: 1

Author

N. J. A. Sloane, Oct 17 2013

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Jorge Luis Cimadevilla Villacorta, Certain inequalities associated with the divisor function, Amer. Math. Monthly, 120 (2013), 832-837. (Shows that a(n) >= 0.)

Crossrefs

Cf. A000005, A230290, A230291, A230293, A230294, A230295, A230296, A230476.

Programs

Maple

See A230290.

Mathematica

Accumulate[Table[DivisorSigma[0, 24*n + 9] - DivisorSigma[0, 6*n + 3], {n, 1, 100}]] (* Amiram Eldar, Apr 12 2024 *)

PARI

vector(100, n, sum(i=1, n, numdiv(24*i+9)) - sum(i=1, n, numdiv(6*i+3))) \\ Michel Marcus, Oct 09 2014

Formula

a(n) = (5*log(2)/3) * n + O(n^(1/3)*log(n)). - Amiram Eldar, Apr 12 2024