A225959 a(n) = sigma(2*n^3) - sigma(n^3).
2, 16, 80, 128, 312, 640, 800, 1024, 2186, 2496, 2928, 5120, 4760, 6400, 12480, 8192, 10440, 17488, 14480, 19968, 32000, 23424, 25440, 40960, 39062, 38080, 59048, 51200, 50520, 99840, 61568, 65536, 117120, 83520, 124800, 139904, 104120, 115840, 190400, 159744, 141288, 256000
Offset: 1
Keywords
Examples
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 +... where 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 +... 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 +...
Links
- Paul D. Hanna, Table of n, a(n) for n = 1..1000
Programs
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Mathematica
a[n_] := DivisorSigma[1, 2*n^3] - DivisorSigma[1, n^3]; Array[a, 50] (* Amiram Eldar, Mar 17 2024 *)
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PARI
{a(n)=sigma(2*n^3)-sigma(n^3)} for(n=1, 50, print1(a(n), ", "))
Formula
a(n) = A054785(n^3).
Logarithmic derivative of A225958.
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
Comments