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 A354525 #22 Jun 16 2023 03:17:04 %S A354525 1,2,3,5,6,7,9,11,13,14,15,17,19,21,23,25,29,31,33,35,37,41,43,45,47, %T A354525 49,51,53,55,59,61,62,67,69,71,73,77,79,83,85,89,91,93,95,97,101,103, %U A354525 107,109,113,115,119,121,127,131,133,137,139,141,143,145,149,151,155,157 %N A354525 Numbers k such that A354512(k) = A001221(k). %C A354525 Numbers k such that for every prime factor p of k we have gpf(k+p) = p, gpf = A006530. %C A354525 Numbers k such that for every prime factor p of k, k+p is p-smooth. %C A354525 If k is an even term, then k+2 is a power of 2, so k is of the form 2*(2^m-1). Those m for which 2*(2^m-1) is a term are listed in A354531. %H A354525 Jianing Song, <a href="/A354525/b354525.txt">Table of n, a(n) for n = 1..8435</a> (all terms <= 50000) %e A354525 15 is a term since the prime factors of 15 are 3,5, and we have gpf(15+3) = 3 and gpf(15+5) = 5. %o A354525 (PARI) gpf(n) = vecmax(factor(n)[, 1]); %o A354525 isA354525(n) = my(f=factor(n)[, 1]); for(i=1, #f, if(gpf(n+f[i])!=f[i], return(0))); 1 %Y A354525 Cf. A001221, A354512, A006530, A354531, A354532, A354533, A354534. %Y A354525 Indices of 0 in A354527. Complement of A354526. %K A354525 nonn,easy %O A354525 1,2 %A A354525 _Jianing Song_, Aug 16 2022