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A280208 Numbers n such that 4^n - 3^n is not squarefree, but 4^d - 3^d is squarefree for every proper divisor d of n. 5
4, 14, 55, 78, 111 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Where numbers n such that 4^n - 3^n is not squarefree: numbers of the form i*a(j) for i >= 1.

The smallest squares of 4^n - 3^n as defined above are 25, 49, 121, 169, 1369. - Robert Price, Mar 07 2017

LINKS

Table of n, a(n) for n=1..5.

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 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), A280203 (k = 2), this sequence (k = 3), A280209 (k = 4).

Sequence in context: A302171 A045501 A162481 * A088655 A302288 A149490

Adjacent sequences:  A280205 A280206 A280207 * A280209 A280210 A280211

KEYWORD

nonn,more

AUTHOR

Juri-Stepan Gerasimov, Dec 28 2016

STATUS

approved

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Last modified February 22 23:14 EST 2020. Contains 332157 sequences. (Running on oeis4.)