A295012 a(n) = sigma(12n - 1)/12, where sigma = sum of divisors (A000203).

1, 2, 4, 4, 5, 6, 7, 10, 9, 12, 11, 14, 16, 14, 15, 16, 20, 22, 19, 20, 21, 22, 31, 28, 28, 26, 30, 34, 29, 30, 36, 32, 40, 38, 35, 36, 37, 56, 39, 40, 41, 42, 52, 48, 57, 50, 47, 62, 49, 50, 56, 60, 64, 54, 55, 62, 57, 70, 68, 60, 66, 62, 76, 70, 70, 76

Offset

1,2

Comments

Robert G. Wilson v observes in A280098 that {1, 3, 4, 6, 8, 12, 24} seem to be the only positive integers k such that sigma(kn-1)/k is an integer for all n > 0.

Links

Muniru A Asiru, Table of n, a(n) for n = 1..100000

Formula

Sum_{k=1..n} a(k) = c * n^2 + O(n*log(n)), where c = Pi^2/18 = 0.548311... (A086463). - Amiram Eldar, Mar 28 2024

Maple

with(numtheory):
seq(sigma(12*n-1)/12, n=1..10^3); # Muniru A Asiru, Dec 28 2017

Mathematica

Array[DivisorSigma[1, 12 # - 1]/12 &, 66] (* Michael De Vlieger, Dec 08 2017 *)

Prog

(PARI) vector(90, n, sigma(12*n-1)/12)
(GAP) sequence := List([1..10^5], n-> Sigma(12 *n-1)/12); # Muniru A Asiru, Dec 28 2017

Crossrefs

Cf. A280098 (analog for k = 24), A097723 (analog for k = 4), A033686 (analog for k = 3), A000203 (sigma, also the analog for k = 1).

The analog for k = 8 is A258835, up to the offset.

The analog for k = 6 is A098098 (up to the offset), a signed variant of this and the preceding one is A258831.

Cf. A086463.

Sequence in context: A214880 A071193 A071192 * A308629 A100921 A140201

Adjacent sequences: A295009 A295010 A295011 * A295013 A295014 A295015

Keyword

nonn,easy

Author

M. F. Hasler, Dec 08 2017

Status

approved