

A057896


Nonnegative numbers that can be written as m^k  m (with m and k nonnegative) in more than one way.


3




OFFSET

1,2


COMMENTS

The next term, if it exists, is at least 2*10^17.  David Wasserman, May 01 2002
a(10) > 10^24, if it exists. The only numbers below 10^24 that can be written as m^k+m in more than one way are 30 = 5^2+5 = 3^3+3 and 130 = 5^3+5 = 2^7+2.  Giovanni Resta, Jun 21 2018
Conjectured to be finite and complete by Bennett (2001).


LINKS

Table of n, a(n) for n=1..9.
Michael Bennett, On some exponential equations of S. S. Pillai, Canad. J. Math. 53 (2001), 897922.
Brady Haran and Matt Parker, Why 1980 was a great year to be born... but 2184 will be better, Numberphile video (2015).
Dana Mackenzie, 2184: An Absurd (and Adsurd) Tale, Integers (Electronic Journal of Combinatorial Number Theory), 18 (2018), A33. See Conjecture 3.


EXAMPLE

30 is in the sequence since 30 = 2^5  2 = 6^2  6;
2184 is in the sequence since 2184 = 3^7  3 = 13^3  13.


MAPLE

res:= {0}:
for k from 3 to 60 do
for m from 2 while m^km < 2^60 do
x:= m^km;
if assigned(R[x]) or issqr(4*x+1) then res:= res union {x}
else R[x]:= [m, k]
fi
od
od:
res; # Robert Israel, Oct 07 2015


CROSSREFS

Cf. A000918, A057895, A308324.
Sequence in context: A325950 A275953 A322170 * A147779 A054721 A074111
Adjacent sequences: A057893 A057894 A057895 * A057897 A057898 A057899


KEYWORD

more,nonn


AUTHOR

Henry Bottomley, Sep 26 2000


EXTENSIONS

More terms from Jud McCranie, Oct 01 2000
Offset corrected by Joerg Arndt, Oct 07 2015


STATUS

approved



