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 A344315 #18 May 22 2021 04:39:04
%S A344315 1,27,135,2511,2295,6975,5264,12393728,12375,2200933376,108224,257499,
%T A344315 170624,3684603215871,4402431,2035980763136,126224,41680575,701443071,
%U A344315 46977524,1245375,2707370000,4388175,3129761024,1890944
%N A344315 a(n) is the least number k such that A048105(k) = A048105(k+1) = 2*n, and 0 if it does not exist.
%C A344315 There are no two consecutive numbers with an odd number of non-unitary divisors, since A048105(k) is odd only if k is a perfect square.
%C A344315 a(25) <= 1965640805422351777791, a(26) <= 3127059999. In general, a(n) <= A215199(n+1). - _Daniel Suteu_, May 20 2021
%e A344315 a(0) = 1 since A048105(1) = A048105(2) = 0.
%e A344315 a(1) = 27 since A048105(27) = A048105(28) = 2.
%t A344315 nd[n_] := DivisorSigma[0, n] - 2^PrimeNu[n]; seq[max_] := Module[{s = Table[0, {max}], k = 2, c = 0, nd1 = 0}, While[c < max, If[(nd2 = nd[k]) == nd1 && nd2 < 2*max && s[[nd2/2 + 1]] == 0, c++; s[[nd2/2 + 1]] = k - 1]; nd1 = nd2; k++]; s]; seq[7]
%o A344315 (PARI)
%o A344315 A048105(n) = numdiv(n) - 2^omega(n);
%o A344315 isok(n,k) = A048105(k) == 2*n && A048105(k+1) == 2*n;
%o A344315 a(n) = for(k=1, oo, if(isok(n, k), return(k))); \\ _Daniel Suteu_, May 16 2021
%Y A344315 Cf. A048105, A075036, A093548, A309181, A344314.
%K A344315 nonn,more
%O A344315 0,2
%A A344315 _Amiram Eldar_, May 14 2021
%E A344315 a(13)-a(24) confirmed by _Martin Ehrenstein_, May 20 2021