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%I #17 Dec 24 2022 11:14:18
%S 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 69,71,73,77,79,81,83,87,89,91,93,97,99
%N Numbers k such that the squarefree kernel of 9^k*(9^k - 1) is 3*(9^k - 1)/4.
%C From _Artur Jasinski_: (Start)
%C 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 Conjecture: This sequence is infinite. (End)
%o (PARI) rad(n) = factorback(factor(n)[, 1]); \\ A007947
%o isok(k) = rad(9^k*(9^k - 1)) == 3*(9^k - 1)/4; \\ _Michel Marcus_, Dec 24 2022
%Y Cf. A007947, A054880
%K nonn,hard,more
%O 1,2
%A _Artur Jasinski_, Jan 29 2010
%E Edited by _Jon E. Schoenfield_, Dec 23 2022
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