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 A356743 #10 Aug 25 2022 09:13:32 %S A356743 18,50,242,243,423,475,603,637,722,845,925,1682,1773,2007,2523,2525, %T A356743 2527,3123,3175,3177,4203,4475,4525,4923,5823,6725,6811,6962,7299, %U A356743 7442,7675,8425,8957,8973,9457,9925,10051,10082,10467,11673,11709,12427,12482,12591,13023,13075 %N A356743 Numbers k such that k and k+2 both have exactly 6 divisors. %C A356743 If an even number has exactly 6 divisors, then it is of the form 32, 4*p or 2*p^2 for an odd prime p. Note that 4*p + 2 = 2*q^2 is impossible since q^2 - 1 is divisible by 24 for prime q >= 5. As a result, if k is an even term, then it is of the form 2*p^2 such that (p^2+1)/2 is a prime (p is in A048161). %H A356743 Jianing Song, <a href="/A356743/b356743.txt">Table of n, a(n) for n = 1..10000</a> %e A356743 50 is a term since 50 and 52 both have 6 divisors. %o A356743 (PARI) isA356743(n) = numdiv(n)==6 && numdiv(n+2)==6 %Y A356743 Cf. A048161. %Y A356743 Numbers k such that k and k+2 both have exactly m divisors: A001359 (m=2), A356742 (m=4), this sequence (m=6), A356744 (m=8). %Y A356743 Cf. also A049103 (numbers k such that k and k+1 both have exactly 6 divisors). %K A356743 nonn %O A356743 1,1 %A A356743 _Jianing Song_, Aug 25 2022