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

1,2

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.

Formula

a(n) = A361316(A063947(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}]]; s[1] = 1; s[n_] := n * Times @@ f @@@ FactorInteger[n]; Select[Array[s, 10^4], IntegerQ]

Prog

(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, ", "))); }

Crossrefs

Cf. A063947, A361316, A361317.

Similar sequences: A001600, A006087.

Sequence in context: A178993 A193768 A361784 * A205791 A039696 A076332

Adjacent sequences: A361315 A361316 A361317 * A361319 A361320 A361321

Keyword

nonn

Author

Amiram Eldar, Mar 09 2023

Status

approved