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

Author

Benoit Cloitre, Sep 07 2002

Keywords

• nonn

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

Crossrefs

Cf. A027612, A064169.

Cf. A096617, A001008.

Programs

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 *)

Formula

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

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

Extensions

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

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