A230296 a(n) = Sum_{i=1..n} d(72*i+1) - Sum_{i=1..n} d(18*i+1), where d(n) = A000005(n).

0, 2, 2, 3, 2, 2, 4, 2, 4, 6, 8, 8, 6, 4, 6, 5, 12, 8, 7, 8, 10, 12, 10, 16, 14, 12, 14, 12, 12, 12, 16, 18, 12, 14, 14, 12, 16, 20, 19, 19, 19, 26, 24, 22, 24, 24, 22, 20, 20, 20, 20, 26, 26, 24, 26, 28, 28, 22, 24, 24, 24, 30, 30, 32, 34, 36, 38, 33, 31, 30, 30, 36, 36, 35, 35, 36, 36, 36, 36, 36, 38, 38, 34, 34

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, A230292, A230293, A230294, A230295, A230476.

Programs

Maple

See A230290.

Mathematica

Accumulate[Table[DivisorSigma[0, 72*n + 1] - DivisorSigma[0, 18*n + 1], {n, 1, 100}]] (* Amiram Eldar, Apr 12 2024 *)

PARI

vector(100, n, sum(i=1, n, numdiv(72*i+1)) - sum(i=1, n, numdiv(18*i+1))) \\ Michel Marcus, Oct 09 2014

Formula

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