A361384 a(n) is the number of distinct prime factors of the n-th unitary harmonic number.

0, 2, 2, 3, 3, 4, 4, 3, 4, 5, 4, 5, 4, 3, 4, 5, 4, 5, 4, 4, 3, 5, 4, 5, 5, 5, 5, 5, 5, 4, 5, 5, 4, 5, 5, 5, 5, 4, 4, 4, 5, 6, 5, 6, 5, 5, 6, 6, 5, 5, 6, 6, 5, 5, 6, 6, 6, 6, 5, 6, 5, 6, 6, 6, 5, 6, 5, 6, 5, 6, 5, 6, 4, 5, 6, 6, 6, 6, 5, 6, 5, 6, 6, 6, 6, 5, 6

Offset

1,2

Comments

Each term appears a finite number of times in the sequence (Hagis and Lord, 1975).

Links

Amiram Eldar, Table of n, a(n) for n = 1..290

Peter Hagis, Jr. and Graham Lord, Unitary harmonic numbers, Proc. Amer. Math. Soc., Vol. 51, No. 1 (1975), pp. 1-7.

Formula

a(n) = A001221(A006086(n)).

Mathematica

uh[n_] := n * Times @@ (2/(1 + Power @@@ FactorInteger[n])); uh[1] = 1; PrimeNu[Select[Range[10^6], IntegerQ[uh[#]] &]]

Prog

(PARI) uhmean(n) = {my(f = factor(n)); n*prod(i=1, #f~, 2/(1+f[i, 1]^f[i, 2])); };
lista(kmax) = {my(uh); for(k = 1, kmax, uh = uhmean(k); if(denominator(uh) == 1, print1(omega(k), ", "))); }

Crossrefs

Cf. A001221, A006086, A006087.

Sequence in context: A340321 A340320 A059998 * A339731 A234475 A339082

Adjacent sequences: A361381 A361382 A361383 * A361385 A361386 A361387

Keyword

nonn

Author

Amiram Eldar, Mar 10 2023

Status

approved