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A280203 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. 7

%I #25 Jul 21 2020 02:30:05

%S 10,11,42,52,57,203,272,497

%N 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.

%C Primitive members of A280149: members of A280149 which are not multiples of any earlier term.

%C 547 <= a(9) <= 689. 689, 732, 776, 903, 1055, 1081, 1332, 2525, 2628 are terms. - _Chai Wah Wu_, Jul 20 2020

%e 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.

%t 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 *)

%o (PARI) is(n)=fordiv(n,d, if(!issquarefree(3^d-2^d), return(d==n))); 0 \\ _Charles R Greathouse IV_, Mar 01 2018

%Y Cf. A001047, A280149.

%Y 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).

%K nonn,more

%O 1,1

%A _Juri-Stepan Gerasimov_ and _Charles R Greathouse IV_, Dec 28 2016

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Last modified March 28 12:26 EDT 2024. Contains 371254 sequences. (Running on oeis4.)