A098985 -id:A098985 - cp's OEIS frontend

A098986 Numerators (divided by 2) in series expansion of log( Sum_{m=-oo,oo} q^(m^2) ).

0, 1, -1, 4, -1, 6, -4, 8, -1, 13, -6, 12, -4, 14, -8, 8, -1, 18, -13, 20, -6, 32, -12, 24, -4, 31, -14, 40, -8, 30, -8, 32, -1, 16, -18, 48, -13, 38, -20, 56, -6, 42, -32, 44, -12, 26, -24, 48, -4, 57, -31, 24, -14, 54, -40, 72, -8, 80, -30, 60, -8, 62, -32, 104, -1, 84, -16, 68, -18, 32, -48, 72, -13, 74, -38, 124, -20, 96

Offset: 0

N. J. A. Sloane, Oct 24 2004

			2*q-2*q^2+8/3*q^3-2*q^4+12/5*q^5-8/3*q^6+16/7*q^7-2*q^8+26/9*q^9-...

Cf. A000122, A098985, A098984.

Numerator[CoefficientList[Series[Log[Sum[q^m^2, {m, -Infinity, Infinity}]], {q, 0, 77}], q]]/2 (* L. Edson Jeffery, Jul 14 2014 *)

A098984 Numerators in series expansion of log( Sum_{m=-oo,oo} q^(m^2) ).

Original entry on oeis.org

0, 2, -2, 8, -2, 12, -8, 16, -2, 26, -12, 24, -8, 28, -16, 16, -2, 36, -26, 40, -12, 64, -24, 48, -8, 62, -28, 80, -16, 60, -16, 64, -2, 32, -36, 96, -26, 76, -40, 112, -12, 84, -64, 88, -24, 52, -48, 96, -8, 114, -62, 48, -28, 108, -80, 144, -16, 160, -60, 120, -16, 124, -64, 208, -2, 168, -32, 136, -36, 64, -96, 144

Offset: 0

N. J. A. Sloane, Oct 24 2004

			2*q-2*q^2+8/3*q^3-2*q^4+12/5*q^5-8/3*q^6+16/7*q^7-2*q^8+26/9*q^9-...

Cf. A000122, A098985, A098986.

Numerator[CoefficientList[Series[Log[Sum[q^m^2, {m, -Infinity, Infinity}]], {q, 0, 77}], q]]  (* L. Edson Jeffery, Jul 14 2014 *)

A336113 a(n) is the numerator of Sum_{odd d|n} 1/d.

Original entry on oeis.org

1, 1, 4, 1, 6, 4, 8, 1, 13, 6, 12, 4, 14, 8, 8, 1, 18, 13, 20, 6, 32, 12, 24, 4, 31, 14, 40, 8, 30, 8, 32, 1, 16, 18, 48, 13, 38, 20, 56, 6, 42, 32, 44, 12, 26, 24, 48, 4, 57, 31, 24, 14, 54, 40, 72, 8, 80, 30, 60, 8, 62, 32, 104, 1, 84, 16, 68, 18, 32, 48, 72

Offset: 1

Michel Marcus, Jul 09 2020

			1, 1, 4/3, 1, 6/5, 4/3, 8/7, 1, 13/9, 6/5, 12/11, 4/3, 14/13, 8/7, 8/5, 1, ...

Sumit Kumar Jha, An identity for the sum of inverses of odd divisors of n in terms of the number of representations of n as a sum of r squares, arXiv:2007.04243 [math.GM], 2020.

Cf. A098985 (denominators), A098986.

a[n_] := Numerator @ DivisorSum[n, 1/# &, OddQ[#] &]; Array[a, 100] (* Amiram Eldar, Jul 09 2020 *)

a(n) = numerator(sumdiv(n, d, if (d%2, 1/d)));

a(n) = (-1)^(n+1) * A098986(n) for n>=1.

cp's OEIS Frontend

A098986 Numerators (divided by 2) in series expansion of log( Sum_{m=-oo,oo} q^(m^2) ).

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A098984 Numerators in series expansion of log( Sum_{m=-oo,oo} q^(m^2) ).

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Author

Keywords

Examples

Crossrefs

Programs

Mathematica

A336113 a(n) is the numerator of Sum_{odd d|n} 1/d.

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