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%I #25 Dec 22 2023 08:05:42
%S 1,1,1,2,2,2,1,1,2,1,1,2,1,2,1,1,2,1,4,1,1,2,2,3,1,2,1,2,2,1,1,2,2,2,
%T 1,1,1,1,4,2,1,2,1,2,2,1,3,1,3,2,1,2,2,4,1,2,1,2,2,1,4,1,1,2,1,1,1,2,
%U 2,2,2,2,2,3,2,1,1,1,2,2,2,2,2,4,1,1
%N Number of divisors of 24*n - 1 divided by 2.
%C It appears that this sequence has the same parity as the spt function A092269 (See A195053). - _Omar E. Pol_, Jan 30 2012
%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))/2 = A195051(n)/2.
%F Sum_{k=1..n} a(k) ~ (n/6) * (log(n) + 2*gamma - 1 + 5*log(2) + 2*log(3)), where gamma is Euler's constant (A001620). - _Amiram Eldar_, Dec 22 2023
%t a[n_] := DivisorSigma[0, 24*n-1]/2; Array[a, 100] (* _Amiram Eldar_, Dec 22 2023 *)
%o (PARI) a(n) = numdiv(24*n-1)/2; \\ _Amiram Eldar_, Dec 22 2023
%Y Cf. A000005, A001620, A092269, A134517, A183010, A183011, A195051, A195053.
%K nonn,easy
%O 1,4
%A _Omar E. Pol_, Jan 13 2012