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A225959 a(n) = sigma(2*n^3) - sigma(n^3).

%I A225959 #13 Mar 17 2024 03:19:39
%S A225959 2,16,80,128,312,640,800,1024,2186,2496,2928,5120,4760,6400,12480,
%T A225959 8192,10440,17488,14480,19968,32000,23424,25440,40960,39062,38080,
%U A225959 59048,51200,50520,99840,61568,65536,117120,83520,124800,139904,104120,115840,190400,159744,141288,256000
%N A225959 a(n) = sigma(2*n^3) - sigma(n^3).
%C A225959 Here sigma(n) = A000203(n), the sum of the divisors of n.
%H A225959 Paul D. Hanna, <a href="/A225959/b225959.txt">Table of n, a(n) for n = 1..1000</a>
%F A225959 a(n) = A054785(n^3).
%F A225959 Logarithmic derivative of A225958.
%F A225959 Sum_{k=1..n} a(k) ~ c * n^4, where c = (15/44) * zeta(4) * Product_{p prime} (1 + 1/p^2 + 1/p^3) = (15/44) * A013662 * A330595 = 0.64531050605789193162... . - _Amiram Eldar_, Mar 17 2024
%e A225959 L.g.f.: L(x) = 2*x + 16*x^2/2 + 80*x^3/3 + 128*x^4/4 + 312*x^5/5 + 640*x^6/6 +...
%e A225959 where
%e A225959 exp(L(x)) = 1 + 2*x + 10*x^2 + 44*x^3 + 134*x^4 + 468*x^5 + 1524*x^6 + 4584*x^7 + 13862*x^8 +...+ A225958(n)*x^n +...
%e A225959 exp(-L(-x)) = 1 + 2*x - 6*x^2 + 12*x^3 + 38*x^4 - 108*x^5 + 148*x^6 + 168*x^7 +...+ A225957(n)*x^n +...
%t A225959 a[n_] := DivisorSigma[1, 2*n^3] - DivisorSigma[1, n^3]; Array[a, 50] (* _Amiram Eldar_, Mar 17 2024 *)
%o A225959 (PARI) {a(n)=sigma(2*n^3)-sigma(n^3)}
%o A225959 for(n=1, 50, print1(a(n), ", "))
%Y A225959 Cf. A225958, A225957, A000203, A224903.
%Y A225959 Cf. A013662, A330595.
%K A225959 nonn
%O A225959 1,1
%A A225959 _Paul D. Hanna_, May 22 2013