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 A172253 #20 Jun 15 2024 19:37:36 %S A172253 1,3,7,9,11,13,17,19,23,27,29,31,33,37,41,43,47,49,51,53,57,59,61,67, %T A172253 69,71,73,77,79,81,83,87,89,91,93,97,99,101,103,107,109,111,113,119, %U A172253 121,123,127,129,131,133,137,139,141,143,149,151,153,157,159,161 %N A172253 Numbers k such that the squarefree kernel of 9^k*(9^k - 1) is 3*(9^k - 1)/4. %C A172253 From _Artur Jasinski_: (Start) %C A172253 The maximal value of the squarefree kernel of a*b*9^k for every number 9^k and every a,b such that a + b = 9^k and gcd(a,b,3)=1 is never less than 3*(9^k - 1)/4 and is exactly equal to 3*(9^k - 1)/4 for exponents k in this sequence. %C A172253 Conjecture: This sequence is infinite. (End) %o A172253 (PARI) rad(n) = factorback(factor(n)[, 1]); \\ A007947 %o A172253 isok(k) = rad(9^k*(9^k - 1)) == 3*(9^k - 1)/4; \\ _Michel Marcus_, Dec 24 2022 %Y A172253 Cf. A007947, A054880 %K A172253 nonn,hard %O A172253 1,2 %A A172253 _Artur Jasinski_, Jan 29 2010 %E A172253 Edited by _Jon E. Schoenfield_, Dec 23 2022 %E A172253 More terms from _Sean A. Irvine_, Jun 15 2024