

A101051


n = p(1)^m(1) * p(2)^m(2) ... *p(k)^m(k) = p(1)^r(1) + p(2)^r(2) ... + p(k)^r(k), p(1),...,p(k) primes of the factorization of n, m(i) the exponent of prime p(i), r(i) smallest primitive root of p(i) i = 1..k n < 1.0e6.


0



2, 9, 25, 121, 132, 169, 343, 361, 841, 1369, 2809, 3481, 3721, 4489, 4913, 6889, 10201, 11449, 16371, 17161, 19321, 22201, 26569, 29791, 29929, 32041, 32761, 38809, 44521, 51529, 72361, 79507, 85849, 100489, 120409, 121801, 139129, 143641
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

Most elements of the sequence have k = 1, only 132 and 16371 with k=3 are found. Further searches did not find any more elements with k >= 3. k has to be odd in any case, this can be easily seen by looking at the parity of the prime factors. Perhaps someone with a stronger computer can find more numbers with k>1, if there are any.


LINKS

Table of n, a(n) for n=1..38.


EXAMPLE

16371 = 3^2 * 17 * 107 = 3^2 + 17^3 + 107^2


CROSSREFS

Sequence in context: A124633 A093122 A305351 * A218460 A085070 A083383
Adjacent sequences: A101048 A101049 A101050 * A101052 A101053 A101054


KEYWORD

nonn


AUTHOR

Sven Simon, Nov 28 2004


STATUS

approved



