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#128 by N. J. A. Sloane at Sun Jul 02 13:37:48 EDT 2023
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#127 by Michael Somos at Sat Jul 01 17:34:53 EDT 2023
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#126 by Michael Somos at Sat Jul 01 17:34:36 EDT 2023
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Expansion of (-1/2) x (d phi(-x) / dx) / phi(-x) in powers of x where phi() is a Ramanujan theta function. - Michael Somos, Jul 01 2023
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| STATUS
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approved
editing
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Discussion
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| Sat Jul 01
| 17:34
| Michael Somos: Added more info.
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#125 by Charles R Greathouse IV at Thu Sep 08 08:44:29 EDT 2022
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(MAGMAMagma) [&+[d:d in Divisors(m)|IsOdd(Floor(m/d))] :m in [1..75]]; // Marius A. Burtea, Aug 12 2019
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Discussion
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| Thu Sep 08
| 08:44
| OEIS Server: https://oeis.org/edit/global/2944
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#124 by Alois P. Heinz at Fri Dec 17 16:46:04 EST 2021
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#123 by Chai Wah Wu at Fri Dec 17 15:38:58 EST 2021
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#122 by Chai Wah Wu at Fri Dec 17 15:38:49 EST 2021
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(Python)
from math import prod
from sympy import factorint
def A002131(n): return prod(p**e if p == 2 else (p**(e+1)-1)//(p-1) for p, e in factorint(n).items()) # Chai Wah Wu, Dec 17 2021
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approved
editing
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#121 by N. J. A. Sloane at Mon Jan 11 23:18:04 EST 2021
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#120 by Peter Bala at Sun Jan 10 07:00:31 EST 2021
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#119 by Peter Bala at Sun Jan 10 06:22:37 EST 2021
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a(2*n) = 2*a(n); a(2*n+1) = A008438(n).). (End)
The sequence (a(2*n+1)) = [1, 4, 6, 8, 13, 12, 14, ...] appears to have the g.f. Sum_{n = -oo..oo} x^(3*n+1)/(1 - x^(2*n+1))^2. (End)
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A diagonal of A060047. Bisection A008438.
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proposed
editing
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