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 A280208 Numbers m such that 4^m - 3^m is not squarefree, but 4^d - 3^d is squarefree for every proper divisor d of m. 5
 4, 14, 55, 78, 111, 253, 342, 355 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Where numbers m such that 4^m - 3^m is not squarefree: numbers of the form i*a(j) for i >= 1. The smallest squares of 4^m - 3^m as defined above are 25, 49, 121, 169, 1369, 529, 361, 5041. - Robert Price, Mar 07 2017 431 <= a(9) <= 1081. 1081, 3403 are terms. - Chai Wah Wu, Jul 20 2020 LINKS EXAMPLE 4 is in this sequence because all 4^1 - 3^1 = 1, 4^2 - 3^2 = 7 are squarefrees where 1, 2 are proper divisors of 4 and 4^4 - 3^4 = 175 = 7*5^2 is not squarefree; 14 is in this sequence because all 4^1 = 3^2 = 1, 4^2 - 3^2 = 7, 4^7 - 3^7 = 14197 are squarefrees where 1, 2, 7 are proper divisors of 14 and 4^14 - 3^14 = 263652487 = 7^2*3591*14197 is not squarefree. MATHEMATICA Function[s, DeleteCases[#, 0] &@ MapIndexed[#1 Boole[! AnyTrue[Take[s, First@ #2 - 1], Function[k, Divisible[#1, k]]]] &, s]]@ Select[Range@ 80, ! SquareFreeQ[4^# - 3^#] &] (* Michael De Vlieger, Dec 30 2016 *) CROSSREFS Cf. A005061. Cf. Numbers m such that (k+1)^m - k^m is not squarefree, but (k+1)^d - k^d is squarefree for every proper divisor d of m: A237043 (k = 1), A280203 (k = 2), this sequence (k = 3), A280209 (k = 4), A280307 (k = 6). Sequence in context: A307733 A045501 A162481 * A088655 A302288 A149490 Adjacent sequences: A280205 A280206 A280207 * A280209 A280210 A280211 KEYWORD nonn,more AUTHOR Juri-Stepan Gerasimov, Dec 28 2016 EXTENSIONS a(6)-a(8) from Jinyuan Wang, May 15 2020 STATUS approved

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Last modified December 6 14:43 EST 2022. Contains 358644 sequences. (Running on oeis4.)