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.
%I A083795 #24 Jul 03 2025 10:56:15
%S A083795 3,15,22,27,34,35,39,45,58,76,86,87,94,95,99,105,117,119,123,134,136,
%T A083795 142,143,146,148,159,172,178,190,202,203,206,214,215,218,219,231,232,
%U A083795 243,244,245,254,286,297,299,302,303,327,333,335,345,375,376,382,388
%N A083795 Numbers k such that k and k-1 have the same number of divisors. Numbers not included in A083794.
%C A083795 Also numbers n such that sigma_0(n+1) * sigma_0(n) / (sigma_0(n+1) + sigma_0(n)) = c, c an integer. - _Ctibor O. Zizka_, Nov 01 2008
%C A083795 Heath-Brown proved that this sequence is infinite. Hildebrand and Erdős, Pomerance, & Sárközy show that n sqrt(log log n) << a(n) << n (log log n)^3, where << is Vinogradov notation. - _Charles R Greathouse IV_, Oct 20 2013
%H A083795 Harvey P. Dale, <a href="/A083795/b083795.txt">Table of n, a(n) for n = 1..1000</a>
%H A083795 P. Erdős, <a href="http://www.renyi.hu/~p_erdos/1936-03.pdf">On a problem of Chowla and some related problems</a>, Proc. Cambridge Philos. Soc. 32 (1936), pp. 530-540.
%H A083795 P. Erdős, C. Pomerance, and A. Sárközy, <a href="http://www.math.dartmouth.edu/~carlp/PDF/58.pdf">On locally repeated values of certain arithmetic functions, II</a>, Acta Math. Hungarica 49 (1987), pp. 251-259. [<a href="http://www.renyi.hu/~p_erdos/1987-14.pdf">alternate link</a>]
%H A083795 D. R. Heath-Brown, <a href="http://dx.doi.org/10.1112/S0025579300010743">The divisor function at consecutive integers</a>, Mathematika 31 (1984), pp. 141-149.
%H A083795 Adolf Hildebrand, <a href="http://projecteuclid.org/euclid.pjm/1102690578">The divisor function at consecutive integers</a>, Pacific J. Math. 129:2 (1987), pp. 307-319.
%p A083795 with(numtheory): for n from 3 to 10^3 do if tau(n) = tau(n-1) then printf(`%d,`,n) fi: od:
%t A083795 SequencePosition[DivisorSigma[0,Range[400]],{x_,x_}][[All,2]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Apr 09 2019 *)
%o A083795 (PARI) is(n)=n>2 && numdiv(n)==numdiv(n-1) \\ _Charles R Greathouse IV_, Jul 21 2015
%Y A083795 Cf. A083794.
%K A083795 nonn
%O A083795 1,1
%A A083795 _Amarnath Murthy_, May 07 2003
%E A083795 Corrected and extended by _James Sellers_, May 19 2003