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A359745 Numbers k such that k and k+1 have the same ordered prime signature.

%I A359745 #10 Jan 17 2023 09:23:56
%S A359745 2,14,21,33,34,38,44,57,85,86,93,94,116,118,122,133,135,141,142,145,
%T A359745 158,171,177,201,202,205,213,214,217,218,230,253,285,296,298,301,302,
%U A359745 326,332,334,381,387,393,394,429,434,445,446,453,481,501,514,526,537,542
%N A359745 Numbers k such that k and k+1 have the same ordered prime signature.
%C A359745 The ordered prime signature of a number n is the list of exponents of the distinct prime factors in the prime factorization of n, in the order of the prime factors (A124010).
%H A359745 Amiram Eldar, <a href="/A359745/b359745.txt">Table of n, a(n) for n = 1..10000</a>
%e A359745 14 is a term since 14 = 2^1 * 7^1 and 15 = 3^1 * 5^1 have the same ordered prime signature, (1, 1).
%e A359745 44 is a term since 44 = 2^2 * 11^1 and 45 = 3^2 * 5^1 have the same ordered prime signature, (2, 1).
%e A359745 75 is a term of A052213 but not a term of this sequence, since 75 = 3^1 * 5^2 and 76 = 2^2 * 19^1 have different ordered prime signatures, (1, 2) and (2, 1).
%t A359745 q[n_] := SameQ @@ (FactorInteger[#][[;; , 2]]& /@ (n + {0, 1})); Select[Range[2, 600], q]
%o A359745 (PARI) lista(nmax) = {my(e1 = [], e2); for(n = 2, nmax, e2 = factor(n)[,2]; if(e1 == e2, print1(n-1, ", ")); e1 = e2); }
%Y A359745 Subsequence of A052213.
%Y A359745 A359746 is a subsequence.
%Y A359745 Cf. A124010.
%K A359745 nonn
%O A359745 1,1
%A A359745 _Amiram Eldar_, Jan 13 2023