A129568 a(n) is the number of positive divisors of the numerator of the n-th harmonic number H(n) = Sum_{k=1..n} 1/k.

1, 2, 2, 3, 2, 3, 6, 2, 2, 6, 4, 6, 8, 4, 4, 6, 4, 6, 4, 4, 2, 24, 4, 8, 4, 2, 8, 6, 6, 24, 4, 8, 4, 4, 4, 24, 4, 16, 4, 12, 2, 12, 8, 16, 8, 12, 16, 8, 4, 8, 8, 24, 4, 8, 4, 2, 8, 24, 4, 12, 4, 2, 16, 16, 16, 48, 16, 4, 2, 12, 16, 12, 8, 8, 16, 16, 32, 12, 2, 16, 8, 6, 16, 16, 8, 8, 16, 24, 2

Offset

1,2

Comments

a(n) = A000005(A001008(n)).

Links

Table of n, a(n) for n=1..89.

Maple

with(numtheory): H:=n->sum(1/k, k=1..n): a:=n->tau(numer(H(n))): seq(a(n), n=1..89); # Emeric Deutsch, May 04 2007

Mathematica

DivisorSigma[0, Numerator[HarmonicNumber[Range[90]]]] (* Harvey P. Dale, Feb 01 2012 *)

Prog

(PARI) a(n) = numdiv(numerator(sum(k=1, n, 1/k))); \\ Michel Marcus, Feb 10 2019

Crossrefs

Cf. A000005, A001008, A129567.

Sequence in context: A306997 A056160 A106245 * A177892 A341758 A236433

Adjacent sequences: A129565 A129566 A129567 * A129569 A129570 A129571

Keyword

nonn

Author

Leroy Quet, Apr 22 2007

Extensions

More terms from Emeric Deutsch, May 04 2007

Status

approved