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

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

1,3

Links

Table of n, a(n) for n=1..71.

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.

Formula

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

Example

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, ...

Mathematica

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

Prog

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

Crossrefs

Cf. A098985 (denominators), A098986.

Sequence in context: A327419 A192066 A347385 * A098986 A000593 A115607

Adjacent sequences: A336110 A336111 A336112 * A336114 A336115 A336116

Keyword

nonn,frac

Author

Michel Marcus, Jul 09 2020

Status

approved