A361318 Harmonic means of the infinitary divisors of the infinitary harmonic numbers.

1, 2, 3, 4, 4, 6, 7, 7, 11, 13, 13, 10, 7, 15, 16, 15, 9, 20, 18, 14, 25, 24, 19, 25, 15, 27, 28, 30, 18, 36, 13, 21, 17, 29, 40, 33, 24, 28, 38, 31, 29, 45, 34, 27, 28, 44, 27, 60, 36, 52, 46, 26, 51, 42, 55, 33, 66, 40, 24, 37, 49, 29, 47, 57, 34, 68, 49, 44

Offset: 1

Author

Amiram Eldar, Mar 09 2023

Keywords

• nonn

Comments

Each term appears a finite number of times in the sequence (Hagis and Cohen, 1990).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..239
• Peter Hagis, Jr. and Graeme L. Cohen, Infinitary harmonic numbers, Bull. Australian Math. Soc., Vol. 41, No. 1 (1990), pp. 151-158.

Crossrefs

Cf. A063947, A361316, A361317.

Similar sequences: A001600, A006087.

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}]]; s[1] = 1; s[n_] := n * Times @@ f @@@ FactorInteger[n]; Select[Array[s, 10^4], IntegerQ]

PARI

ihmean(n) = {my(f = factor(n), b); 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))); };
lista(kmax) = {my(ih); for(k = 1, kmax, ih = ihmean(k); if(denominator(ih) == 1, print1(ih, ", ")));}

Formula

a(n) = A361316(A063947(n)).