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

1,2

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.

Formula

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

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]

Prog

(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)))); }

Crossrefs

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

Similar sequences: A099378, A103340.

Sequence in context: A274164 A103340 A106615 * A361783 A194736 A333363

Adjacent sequences: A361314 A361315 A361316 * A361318 A361319 A361320

Keyword

nonn,frac

Author

Amiram Eldar, Mar 09 2023

Status

approved