cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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.

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%I A280203 #25 Jul 21 2020 02:30:05
%S A280203 10,11,42,52,57,203,272,497
%N 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.
%C A280203 Primitive members of A280149: members of A280149 which are not multiples of any earlier term.
%C A280203 547 <= a(9) <= 689. 689, 732, 776, 903, 1055, 1081, 1332, 2525, 2628 are terms. - _Chai Wah Wu_, Jul 20 2020
%e A280203 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 A280203 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 A280203 (PARI) is(n)=fordiv(n,d, if(!issquarefree(3^d-2^d), return(d==n))); 0 \\ _Charles R Greathouse IV_, Mar 01 2018
%Y A280203 Cf. A001047, A280149.
%Y A280203 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 A280203 nonn,more
%O A280203 1,1
%A A280203 _Juri-Stepan Gerasimov_ and _Charles R Greathouse IV_, Dec 28 2016