

A308324


Numbers which can be written in the form m^k  m with m an odd prime and k a positive integer.


3



0, 6, 20, 24, 42, 78, 110, 120, 156, 240, 272, 336, 342, 506, 620, 726, 812, 930, 1320, 1332, 1640, 1806, 2162, 2184, 2394, 2756, 3120, 3422, 3660, 4422, 4896, 4970, 5256, 6162, 6558, 6806, 6840, 7832, 9312
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Besides the trivial example a(1)=0, the only known term which has two representations is a(24) = 2184 = 3^7  3 = 13^3  13. It is conjectured by Bennett to be the only term with this property.


LINKS

Table of n, a(n) for n=1..39.
Michael Bennett, On some exponential equations of S. S. Pillai, Canad. J. Math. 53 (2001), 897922.
Dana Mackenzie, 2184: An Absurd (and Adsurd) Tale, Integers (Electronic Journal of Combinatorial Number Theory), 18 (2018), A33.


EXAMPLE

a(3) = 5^2  5 = 20.


PROG

(PARI) x=List([]); lim=10000; forprime(m=3, lim, for(k=1, 100, y=(m^km); if(y>lim, break, i=setsearch(x, y, 1); if(i>0, listinsert(x, y, i))))); for(i=1, #x, print(x[i]));


CROSSREFS

Cf. A057895, A246068.
Sequence in context: A103678 A020889 A084682 * A044970 A316291 A090502
Adjacent sequences: A308321 A308322 A308323 * A308325 A308326 A308327


KEYWORD

nonn,easy


AUTHOR

Craig J. Beisel, May 20 2019


STATUS

approved



