A361317 Denominators of the harmonic means of the infinitary divisors of the positive integers.

1, 3, 2, 5, 3, 1, 4, 15, 5, 9, 6, 5, 7, 3, 2, 17, 9, 5, 10, 3, 8, 9, 12, 5, 13, 21, 10, 5, 15, 3, 16, 51, 4, 27, 12, 25, 19, 15, 14, 9, 21, 2, 22, 15, 1, 9, 24, 17, 25, 39, 6, 35, 27, 5, 18, 15, 20, 45, 30, 1, 31, 12, 20, 85, 21, 3, 34, 45, 8, 9, 36, 25, 37, 57

Offset: 1

Author

Amiram Eldar, Mar 09 2023

Keywords

• nonn
• frac

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Peter Hagis, Jr. and Graeme L. Cohen, Infinitary harmonic numbers, Bull. Australian Math. Soc., Vol. 41, No. 1 (1990), pp. 151-158.

Crossrefs

Cf. A037445, A049417, A077609, A063947 (positions of 1's), A361316 (numerators).

Similar sequences: A099378, A103340.

Programs

Mathematica

f[p_, e_] := Module[{b = IntegerDigits[e, 2], m}, m = Length[b]; Product[If[b[[j]] > 0, 2/(1 + p^(2^(m - j))), 1], {j, 1, m}]]; a[1] = 1; a[n_] := Denominator[n * Times @@ f @@@ FactorInteger[n]]; Array[a, 100]

PARI

a(n) = {my(f = factor(n), b); denominator(n * prod(i=1, #f~, b = binary(f[i, 2]); prod(k=1, #b, if(b[k], 2/(f[i, 1]^(2^(#b-k))+1), 1)))); }

Formula

a(n) = denominator(n*A037445(n)/A049417(n)).