A230291 - OEIS

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A230291

a(n) = Sum_{i=1..n} d(24*i+17) - Sum_{i=1..n} d(6*i+5), where d(n) = A000005(n).

0, 2, 2, 2, 0, 2, 4, 6, 6, 4, 4, 4, 6, 6, 6, 6, 10, 10, 10, 10, 10, 12, 10, 10, 8, 6, 12, 14, 16, 16, 16, 18, 16, 18, 16, 14, 16, 16, 16, 12, 18, 22, 22, 24, 20, 22, 22, 24, 22, 20, 22, 28, 26, 26, 26, 24, 26, 26, 26, 26, 24, 28, 30, 30, 30, 30, 34, 34, 36, 32, 32, 32, 34, 36, 32, 34, 36, 34, 34, 34, 36, 36, 40, 42

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

LINKS

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

MAPLE

See A230290.

MATHEMATICA

Accumulate[Table[DivisorSigma[0, 24*n + 17] - DivisorSigma[0, 6*n + 5], {n, 1, 100}]] (* Amiram Eldar, Apr 12 2024 *)

PROG

(PARI) vector(100, n, sum(i=1, n, numdiv(24*i+17)) - sum(i=1, n, numdiv(6*i+5))) \\ Michel Marcus, Oct 09 2014

(Magma) [&+[#Divisors(24*i+17):i in [1..n]]- &+[#Divisors(6*i+5):i in [1..n]]:n in [1..90]]; // Marius A. Burtea, Jan 03 2020

CROSSREFS

Cf. A000005, A230290, A230292, A230293, A230294, A230295, A230296, A230476.

Sequence in context: A274850 A349437 A215594 * A338434 A059288 A319109

Adjacent sequences: A230288 A230289 A230290 * A230292 A230293 A230294

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Oct 17 2013

STATUS

approved