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 A333055 #9 Mar 07 2020 03:51:39 %S A333055 26,104,189,231,242,243,344,374,663,664,735,776,782,874,903,1015,1029, %T A333055 1095,1106,1112,1161,1208,1269,1335,1374,1544,1625,1809,1832,1917, %U A333055 1952,1970,2055,2133,2241,2247,2264,2343,2344,2504,2655,2696,2726,2781,2874,2936 %N A333055 Numbers k such that k and k+1 have different (ordered) prime signatures and d(k) = d(k+1), where d(k) is the number of divisors of k (A000005). %C A333055 Apparently most of the numbers k such that k and k+1 have the same number of divisors (A005237) also have the same prime signature, i.e., they are also terms of A052213 which is a subsequence of A005237. %C A333055 For example, up to 10^8 there are 9593611 terms in A005237, of them only 1573778 (about 16.4%) are not in A052213. This sequence in the complement of A052213 with respect to A005237. %H A333055 Amiram Eldar, <a href="/A333055/b333055.txt">Table of n, a(n) for n = 1..10000</a> %e A333055 26 is a term since 26 = 2 * 13 and 27 = 3^3 have different prime signatures, and d(26) = d(27) = 4. %t A333055 Select[Range[3000], DivisorSigma[0, #] == DivisorSigma[0, #+1] && Sort[FactorInteger[#][[;;,2]]] != Sort[FactorInteger[#+1][[;;,2]]] &] %Y A333055 Cf. A000005, A005237, A052213, A124010, A333056, A333057. %K A333055 nonn %O A333055 1,1 %A A333055 _Amiram Eldar_, Mar 06 2020