
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
