A230294 a(n) = Sum_{i=1..n} d(4*i+1) - Sum_{i=1..n} d(2*i+1), where d(n) = A000005(n).

0, 1, 1, 0, 2, 3, 1, 3, 3, 1, 5, 5, 3, 5, 5, 5, 5, 5, 5, 8, 10, 6, 8, 7, 5, 11, 9, 7, 11, 12, 10, 10, 12, 10, 12, 14, 10, 12, 12, 11, 17, 16, 14, 16, 14, 14, 18, 18, 14, 16, 18, 14, 16, 18, 18, 25, 23, 19, 19, 18, 20, 20, 22, 20, 24, 24, 18, 24, 24, 22, 26, 25, 21, 27, 29, 27, 27, 27, 25, 25, 29, 25, 29, 28, 26, 32

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, A230295, A230296, A230476.

Programs

Maple

See A230290.

Mathematica

Accumulate[Table[DivisorSigma[0, 4*n + 1] - DivisorSigma[0, 2*n + 1], {n, 1, 100}]] (* Amiram Eldar, Apr 12 2024 *)

PARI

vector(100, n, sum(i=1, n, numdiv(4*i+1)) - sum(i=1, n, numdiv(2*i+1))) \\ Michel Marcus, Oct 09 2014

Formula

a(n) = A230476(n) - A230293(n). - Jonathan Sondow, Oct 20 2013

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