A295012 - OEIS

%I #23 Mar 28 2024 09:02:58

%S 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,

%T 26,30,34,29,30,36,32,40,38,35,36,37,56,39,40,41,42,52,48,57,50,47,62,

%U 49,50,56,60,64,54,55,62,57,70,68,60,66,62,76,70,70,76

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

%C _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.

%H Muniru A Asiru, <a href="/A295012/b295012.txt">Table of n, a(n) for n = 1..100000</a>

%F 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

%p with(numtheory):

%p seq(sigma(12*n-1)/12, n=1..10^3); # _Muniru A Asiru_, Dec 28 2017

%t Array[DivisorSigma[1, 12 # - 1]/12 &, 66] (* _Michael De Vlieger_, Dec 08 2017 *)

%o (PARI) vector(90,n,sigma(12*n-1)/12)

%o (GAP) sequence := List([1..10^5], n-> Sigma(12 *n-1)/12); # _Muniru A Asiru_, Dec 28 2017

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

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

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

%Y Cf. A086463.

%K nonn,easy

%O 1,2

%A _M. F. Hasler_, Dec 08 2017