

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




OFFSET

1,1


COMMENTS

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


LINKS



EXAMPLE

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.


MATHEMATICA

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 *)


PROG



CROSSREFS

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).


KEYWORD

nonn,more


AUTHOR



STATUS

approved



