A195051 - OEIS

%I #35 Dec 22 2023 08:03:33

%S 2,2,2,4,4,4,2,2,4,2,2,4,2,4,2,2,4,2,8,2,2,4,4,6,2,4,2,4,4,2,2,4,4,4,

%T 2,2,2,2,8,4,2,4,2,4,4,2,6,2,6,4,2,4,4,8,2,4,2,4,4,2,8,2,2,4,2,2,2,4,

%U 4,4,4,4,4,6,4,2,2,2,4,4,4,4,4,8,2,2

%N Number of divisors of 24*n - 1.

%H Robert Israel, <a href="/A195051/b195051.txt">Table of n, a(n) for n = 1..10000</a>

%H George E. Andrews, Frank G. Garvan, and Jie Liang, <a href="http://dx.doi.org/10.4064/aa158-3-1">Self-conjugate vector partitions and the parity of the spt-function</a>, Acta Arith., Vol. 158, No. 3 (2013), pp. 199-218; <a href="https://eudml.org/doc/279005">alternative link</a>; <a href="https://georgeandrews1.github.io/pdf/289.pdf">author's link</a>.

%F a(n) = A000005(A183010(n)).

%F a(n) = 2 * A195052(n).

%F Sum_{k=1..n} a(k) ~ (n/3) * (log(n) + 2*gamma - 1 + 5*log(2) + 2*log(3)), where gamma is Euler's constant (A001620). - _Amiram Eldar_, Dec 22 2023

%p seq(numtheory:-tau(24*n-1),n=1..100); # _Robert Israel_, Jun 27 2018

%t Table[DivisorSigma[0, 24*n-1], {n, 100}] (* _T. D. Noe_, Jan 14 2012 *)

%o (GAP) List([1..100],n->Tau(24*n-1)); # _Muniru A Asiru_, Jun 27 2018

%o (PARI) a(n) = numdiv(24*n-1); \\ _Amiram Eldar_, Dec 22 2023

%Y Cf. A000005, A001620, A092269, A134517, A183010, A183011, A195052, A195053.

%K nonn,easy

%O 1,1

%A _Omar E. Pol_, Jan 13 2012