A074791 Numbers k such that k does not divide the denominator of the k-th harmonic number.

6, 18, 20, 21, 33, 42, 54, 63, 66, 77, 100, 110, 120, 156, 162, 189, 198, 272, 294, 336, 342, 363, 377, 435, 486, 500, 506, 559, 567, 594, 600, 610, 629, 685, 703, 812, 847, 880, 924, 930, 957, 1067, 1166, 1210, 1243, 1247, 1287, 1320, 1332, 1458, 1590, 1640

Offset

1,1

Comments

k such that A064169(k) is different from A027612(k).

Also k such that A096617(k) is different from A001008(k). - Alexander Adamchuk, Jun 26 2006

This sequence contains A036689(k) for all k > 1. - Wouter van Doorn, Nov 06 2024

Links

Amiram Eldar, Table of n, a(n) for n = 1..2000

Formula

Is a(n) asymptotic to c*n^2 0.5<c<0.7 ?

a(n) < 2*n^2*log(n)^2 for all n > 2. This follows from the fact that for all k > 1 there exists an n such that A036689(k) is equal to A074791(n). - Wouter van Doorn, Nov 06 2024

Mathematica

Select[ Range[1700], Mod[ Denominator[ HarmonicNumber[ # ]], # ] != 0 &] (* Robert G. Wilson v, Sep 28 2005 *)
seq = {}; s = 0; Do[s += 1/n; If[! Divisible[Denominator[s], n], AppendTo[seq, n]], {n, 1, 2000}]; seq (* Amiram Eldar, Dec 01 2020 *)

Crossrefs

Cf. A027612, A064169.

Cf. A096617, A001008.

Sequence in context: A361730 A371989 A045857 * A093106 A234752 A370865

Adjacent sequences: A074788 A074789 A074790 * A074792 A074793 A074794

Keyword

nonn

Author

Benoit Cloitre, Sep 07 2002

Extensions

Better description and more terms from Robert G. Wilson v, Sep 28 2005

Status

approved