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 A140128 #19 Apr 16 2024 02:39:52 %S A140128 2,3,4,14,16,21,26,33,34,35,38,44,57,75,85,86,93,94,98,104,116,118, %T A140128 122,133,135,141,142,145,147,152,153,158,164,170,171,174,175,177,188, %U A140128 189,201,202,205,207,213,214,217,218,225,230,231,242,243,244,245,253,272 %N A140128 A positive integer k is included if d(d(k)) = d(d(k+1)), where d(k) is the number of divisors of k. %H A140128 Ivan Neretin, <a href="/A140128/b140128.txt">Table of n, a(n) for n = 1..10000</a> %F A140128 For m = 2,3,4,5..., a(m) is the smallest integer > a(m-1) such that A010553(a(m)) = A010553(a(m)+1). %e A140128 35 has 4 divisors and 4 has 3 divisors. 36 has 9 divisors and 9 has 3 divisors. Since d(d(35)) = d(d(36)) (=3), then 35 is included in the sequence. %t A140128 Select[Range[250], DivisorSigma[0, DivisorSigma[0, # ]] == DivisorSigma[0, DivisorSigma[0, # + 1]] &] (* _Stefan Steinerberger_, Jun 05 2008 *) %o A140128 (PARI) is(k) = numdiv(numdiv(k)) == numdiv(numdiv(k+1)); \\ _Amiram Eldar_, Apr 16 2024 %Y A140128 Cf. A000005, A010553. %Y A140128 A005237 is a subsequence. %K A140128 nonn %O A140128 1,1 %A A140128 _Leroy Quet_, Jun 04 2008 %E A140128 More terms from _Stefan Steinerberger_, Jun 05 2008 %E A140128 a(56)-a(57) from _Ray Chandler_, Jun 26 2009