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A224903
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a(n) = sigma(2*n^4) - sigma(n^4).
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2
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2, 32, 242, 512, 1562, 3872, 5602, 8192, 19682, 24992, 32210, 61952, 61882, 89632, 189002, 131072, 177482, 314912, 275122, 399872, 677842, 515360, 585122, 991232, 976562, 990112, 1594322, 1434112, 1465082, 3024032, 1908610, 2097152, 3897410, 2839712, 4375162, 5038592, 3852442
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OFFSET
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1,1
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COMMENTS
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Here sigma(n) = A000203(n), the sum of the divisors of n.
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LINKS
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FORMULA
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Sum_{k=1..n} a(k) ~ c * n^5, where c = (31/115) * zeta(5) * Product_{p prime} (1 + 1/p^2 + 1/p^3 + 1/p^5) = 0.51764417195990550114... . - Amiram Eldar, Mar 17 2024
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EXAMPLE
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L.g.f.: L(x) = 2*x + 32*x^2/2 + 242*x^3/3 + 512*x^4/4 + 1562*x^5/5 +...
where exponentiation yields the g.f. of A224902:
exp(L(x)) = 1 + 2*x + 18*x^2 + 114*x^3 + 450*x^4 + 2298*x^5 +...
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MATHEMATICA
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a[n_] := DivisorSigma[1, 2*n^4] - DivisorSigma[1, n^4]; Array[a, 50] (* Amiram Eldar, Mar 17 2024 *)
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PROG
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(PARI) {a(n)=sigma(2*n^4)-sigma(n^4)}
for(n=1, 30, print1(a(n), ", "))
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CROSSREFS
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KEYWORD
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nonn,changed
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AUTHOR
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STATUS
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approved
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