

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




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

Table of n, a(n) for n=1..8.


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

JuriStepan Gerasimov, Dec 28 2016


EXTENSIONS

a(6)a(8) from Jinyuan Wang, May 15 2020


STATUS

approved



