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A172253
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Numbers k such that the squarefree kernel of 9^k*(9^k - 1) is 3*(9^k - 1)/4.
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0
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1, 3, 7, 9, 11, 13, 17, 19, 23, 27, 29, 31, 33, 37, 41, 43, 47, 49, 51, 53, 57, 59, 61, 67, 69, 71, 73, 77, 79, 81, 83, 87, 89, 91, 93, 97, 99
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OFFSET
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1,2
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COMMENTS
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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.
Conjecture: This sequence is infinite. (End)
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LINKS
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PROG
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(PARI) rad(n) = factorback(factor(n)[, 1]); \\ A007947
isok(k) = rad(9^k*(9^k - 1)) == 3*(9^k - 1)/4; \\ Michel Marcus, Dec 24 2022
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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