A338560 Denominators of the fractions f(n) such that (6/Pi^2)*f(n) is the asymptotic density of the numbers k with A280292(k) = sopfr(k) - sopf(k) = n.

1, 1, 6, 12, 12, 360, 72, 560, 2160, 30240, 12600, 399168, 453600, 86486400, 209563200, 1111968000, 363242880, 5557616064000, 163459296000, 70396470144000, 83364240960000, 1773991047628800, 7508350080000, 6120269114319360000, 86090742017280000, 224409867525043200000

Offset: 0

Author

Amiram Eldar, Nov 02 2020

Keywords

• nonn
• frac

Comments

See A338559 for details.

Links

• Amiram Eldar, Table of n, a(n) for n = 0..214

Crossrefs

Cf. A000607, A001414, A001615, A005117, A008472, A013661, A059956, A081770, A280292, A338559 (numerators).

Programs

Mathematica

psi[1] = 1; psi[n_] := n*Times @@ (1 + 1/Transpose[FactorInteger[n]][[1]]); delta[ps_] := 1/psi[(Times @@ ps)*(Times @@ Union[ps])]; f[n_] := Total[delta /@ IntegerPartitions[n, Floor[n/2], Select[Range[n], PrimeQ]]]; Denominator @ Array[f, 30, 0]