login
A361317
Denominators of the harmonic means of the infinitary divisors of the positive integers.
5
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
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
KEYWORD
nonn,frac
AUTHOR
Amiram Eldar, Mar 09 2023
STATUS
approved