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A280209 Numbers n such that 5^n - 4^n is not squarefree, but 5^d - 4^d is squarefree for every proper divisor d of n. 5
2, 55 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Where numbers n such that 5^n - 4^n is not squarefree: numbers of the form i*a(j) for i >= 1.

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): 6, 20, 21, 110, 136, 155, 253, 364, 602, 657, 812, 889, 979, 1081, ... a(15) >= 1207 - Max Alekseyev, Sep 28 2015;

A280203 (k = 2): 10, 11, 42, 52, 57, 203, 272, 497, ... a(9) > 497 - Charles R Greathouse IV, Dec 27 2016;

A280208 (k = 3): 4, 14, 55, 78, 111, ... a(6) >= 139;

this sequence (k = 4): 2, 55, ... a(3) >= 113;

A... (k = 5): 21, 22, 39, ... a(4) >= 97;

A... (k = 6): 20, 26, 55, 68, ... a(5) >= 83;

A... (k = 7): 3, 10, 55, ... a(4) >= 86;

A... (k = 8): 20, 21, 22, 34, ... a(5) >= 73;

A... (k = 9): 33, 38, 42, 78, ... a(5) >= 87;

A... (k = 10): 6, 14, 68, ... a(4) >= 85;

A... (k = 11): 20, 42, 46, 53, ... a(5) >= 79.

The smallest square of 5^n - 4^n as defined above are 9 and 121. - Robert Price, Mar 07 2017

LINKS

Table of n, a(n) for n=1..2.

EXAMPLE

2 is in this sequence because 5^1 - 4^1 = 1 is squarefree where 1 is proper divisor of 2 and 5^2 - 4^2 = 9 = 3^2 is not squarefree.

CROSSREFS

Cf. A005060, A237043, A280203, A280208.

Sequence in context: A117681 A221603 A089180 * A034013 A157262 A007975

Adjacent sequences:  A280206 A280207 A280208 * A280210 A280211 A280212

KEYWORD

bref,nonn,more

AUTHOR

Juri-Stepan Gerasimov, Dec 28 2016

STATUS

approved

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Last modified January 26 01:48 EST 2020. Contains 331270 sequences. (Running on oeis4.)