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A280203
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Numbers n such that 3^n - 2^n is not squarefree, but 3^d - 2^d is squarefree for all proper divisors d of n.
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7
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OFFSET
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1,1
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COMMENTS
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Primitive members of A280149: members of A280149 which are not multiples of any earlier term.
547 <= a(9) <= 689. 689, 732, 776, 903, 1055, 1081, 1332, 2525, 2628 are terms. - Chai Wah Wu, Jul 20 2020
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LINKS
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EXAMPLE
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10 is in this sequence because all 3^1 - 2^1 = 1, 3^2 - 2^2 = 5, 3^5 - 2^5 = 211 are squarefrees and 3^10 - 2^10 = 58025 = 5^2*2321 is not squarefree.
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MATHEMATICA
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Function[s, DeleteCases[#, 0] &@ MapIndexed[#1 Boole[Total@ Boole@ Map[Function[k, Divisible[#1, k]], Take[s, First@ #2 - 1]] == 0] &, s]]@ Select[Range@ 60, ! SquareFreeQ[3^# - 2^#] &] (* Michael De Vlieger, Dec 30 2016 *)
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PROG
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CROSSREFS
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Cf. Numbers n such that (k+1)^n - k^n is not squarefree, but (k+1)^d - k^d is squarefree for every proper divisor d of n: A237043 (k = 1), this sequence (k = 2), A280208 (k = 3), A280209 (k = 4).
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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