A230295 a(n) = Sum_{i=1..n} d(8*i+5) - Sum_{i=1..n} d(4*i+3), where d(n) = A000005(n).

0, 2, 0, 0, 4, 2, 2, 2, 2, 4, 6, 4, 2, 6, 4, 6, 8, 4, 4, 10, 8, 6, 10, 6, 8, 10, 10, 8, 8, 10, 12, 16, 10, 10, 14, 10, 12, 12, 10, 14, 18, 16, 12, 18, 18, 16, 18, 12, 12, 18, 16, 16, 20, 20, 22, 24, 18, 18, 22, 20, 20, 22, 16, 16, 26, 26, 26, 26, 22, 24, 24, 24, 24, 24, 26, 26, 32, 24, 26, 30, 28, 28, 28, 26, 26, 36

Offset

1,2

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.)

Formula

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

Maple

See A230290.

Mathematica

Accumulate[Table[DivisorSigma[0, 8*n + 5] - DivisorSigma[0, 4*n + 3], {n, 1, 100}]] (* Amiram Eldar, Apr 12 2024 *)

Prog

(PARI) vector(100, n, sum(i=1, n, numdiv(8*i+5)) - sum(i=1, n, numdiv(4*i+3))) \\ Michel Marcus, Oct 09 2014

Crossrefs

Cf. A000005, A230290, A230291, A230292, A230293, A230294, A230296, A230476.

Sequence in context: A158118 A212137 A346462 * A147592 A108885 A341654

Adjacent sequences: A230292 A230293 A230294 * A230296 A230297 A230298

Keyword

nonn,changed

Author

N. J. A. Sloane, Oct 17 2013

Status

approved