A230293 a(n) = Sum_{i=1..n} d(8*i+1) - Sum_{i=1..n} d(4*i+1), where d(n) = A000005(n).

1, 0, 1, 3, 1, 1, 3, 3, 3, 6, 2, 1, 7, 5, 6, 6, 4, 6, 8, 7, 6, 8, 8, 8, 10, 6, 8, 15, 11, 10, 10, 8, 8, 14, 12, 11, 17, 15, 15, 15, 11, 10, 16, 14, 15, 17, 13, 19, 21, 19, 17, 17, 19, 17, 22, 15, 15, 21, 21, 23, 21, 21, 21, 27, 23, 22, 24, 20, 22, 28, 22, 21, 31, 25, 23, 27, 25, 28, 30, 28, 26, 28, 30, 30, 30, 26, 28

Offset

1,4

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) = A230476(n) - A230294(n). - Jonathan Sondow, Oct 20 2013

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

Prog

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

Crossrefs

Cf. A000005, A230290, A230291, A230292, A230294, A230295, A230296, A230476.

Sequence in context: A035666 A060592 A080426 * A133116 A059959 A192812

Adjacent sequences: A230290 A230291 A230292 * A230294 A230295 A230296

Keyword

nonn

Author

N. J. A. Sloane, Oct 17 2013

Status

approved