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 A350800 #21 Jan 20 2022 10:31:29
%S A350800 64665,109214,2305557,4701537,6444873,10118654,32225337,33876117,
%T A350800 70282053,105967784,149205914,187434621,268890218,279113505,334925577,
%U A350800 357340922,391392134,424942604,575712494,610752933,612863198,641703842,701792234,743194142,800679495
%N A350800 Numbers k such that k and k+1 have the same number and sum of divisors but a different number of distinct prime factors.
%C A350800 Subsequence of A054004. Most members of A054004 are not a part of this subsequence, so consecutive numbers with equal tau and sigma most often achieve this with an equal count of distinct prime factors.
%H A350800 Amiram Eldar, <a href="/A350800/b350800.txt">Table of n, a(n) for n = 1..223</a> (terms 1..106 from Kevin P. Thompson)
%e A350800 64665 is a term of this sequence since tau(64665) = tau(64666) = 8 and sigma(64665) = sigma(64666) = 2160, but omega(64665) = 4 and omega(64666) = 3.
%t A350800 Select[Range[10^7], DivisorSigma[{0, 1}, #] == DivisorSigma[{0, 1}, # + 1] && PrimeNu[#] != PrimeNu[# + 1] &] (* _Amiram Eldar_, Jan 20 2022 *)
%Y A350800 Cf. A000005, A000203, A001221, A054004.
%K A350800 nonn
%O A350800 1,1
%A A350800 _Kevin P. Thompson_, Jan 16 2022