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#13 by Bruno Berselli at Wed Jul 18 03:02:14 EDT 2018
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#12 by Michel Marcus at Wed Jul 18 01:46:46 EDT 2018
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#11 by G. C. Greubel at Tue Jul 17 22:42:05 EDT 2018
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#10 by G. C. Greubel at Tue Jul 17 22:42:02 EDT 2018
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| LINKS
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G. C. Greubel, <a href="/A203849/b203849.txt">Table of n, a(n) for n = 1..2500</a>
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| MATHEMATICA
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Table[DivisorSigma[2, n]*Fibonacci[n], {n, 50}] (* G. C. Greubel, Jul 17 2018 *)
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| STATUS
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approved
editing
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#9 by Alois P. Heinz at Sat Jan 06 13:24:07 EST 2018
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#8 by Alois P. Heinz at Sat Jan 06 13:24:04 EST 2018
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| NAME
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a(n) = sigma_2(n)*fibonacciFibonacci(n), where sigma_2(n) = A001157(n), the sum of squares of divisors of n.
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| STATUS
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approved
editing
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#7 by Russ Cox at Fri Mar 30 18:37:33 EDT 2012
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| AUTHOR
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_Paul D. Hanna (pauldhanna(AT)juno.com), _, Jan 12 2012
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Discussion
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| Fri Mar 30
| 18:37
| OEIS Server: https://oeis.org/edit/global/213
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#6 by N. J. A. Sloane at Thu Jan 12 09:30:19 EST 2012
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#5 by Paul D. Hanna at Thu Jan 12 00:16:59 EST 2012
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#4 by Paul D. Hanna at Thu Jan 12 00:16:55 EST 2012
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| NAME
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a(n) = sigma_2(n)*fibonacci(n), where sigma_2(n) = A001157(n), the sum of squares of divisors of n.
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| COMMENTS
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Compare g.f. to the Lambert series identity: Sum_{n>=1} n^2*x^n/(1-x^n) = Sum_{n>=1} sigma_2(n)*x^n.
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| FORMULA
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G.f.: Sum_{n>=1} n^2*fibonacci(n)*x^n/(1 - Lucas(n)*x^n + (-1)^n*x^(2*n)) = Sum_{n>=1} sigma_2(n)*fibonacci(n)*x^n, where Lucas(n) = A000204(n).
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| EXAMPLE
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G.f.: A(x) = x + 5*x^2 + 20*x^3 + 63*x^4 + 130*x^5 + 400*x^6 + 650*x^7 +...
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| PROG
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((PARI) {a(n)=sigma(n, 2)*fibonacci(n)}
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| CROSSREFS
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Cf. A203847, A203848, A203838, A001157 (sigma_2), A000204 (Lucas), A000045.
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| STATUS
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proposed
editing
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