cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A094229 Numbers n such that d(n) >= n-th harmonic number H(n)=sum_{i=1..n}1/i.

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%I A094229 #19 May 08 2018 15:11:55
%S A094229 1,2,3,4,6,8,9,10,12,14,15,16,18,20,21,22,24,26,27,28,30,32,36,40,42,
%T A094229 44,45,48,50,52,54,56,60,63,64,66,68,70,72,75,76,78,80,81,84,88,90,92,
%U A094229 96,98,99,100,102,104,105,108,110,112,114,116,117,120,124,126,128,130,132
%N A094229 Numbers n such that d(n) >= n-th harmonic number H(n)=sum_{i=1..n}1/i.
%C A094229 A positive integer n belongs to the sequence if and only the number of its divisors (d(n)) is >= the average number of divisors, in the range from 1 through n, for all positive integers (H(n)).
%C A094229 Visible sharp bend on the graph around the 800th term occur where the n-th harmonic number exceeds 8. - _Ivan Neretin_, Oct 16 2016
%H A094229 Ivan Neretin, <a href="/A094229/b094229.txt">Table of n, a(n) for n = 1..5000</a>
%H A094229 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%H A094229 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 840. (d(n) is given as sigma_0(n).)
%e A094229 6 is in the sequence because the number of its divisors, 4, is greater than the 6th harmonic number, 1/1 + 1/2 + 1/3 + 1/4 + 1/5 + 1/6 = 2.45.
%t A094229 ok[n_] := DivisorSigma[0, n] >= HarmonicNumber[n]; Select[ Range[132], ok] (* _Jean-François Alcover_, Sep 19 2011 *)
%Y A094229 d(n)=A000005(n), H(n)=A001008(n)/A002805(n). See also A004080.
%K A094229 nonn
%O A094229 1,2
%A A094229 _Matthew Vandermast_, May 29 2004