OFFSET
1,1
COMMENTS
Terms that are not divisible by 10 are 78, 102, 156, 174, 182, 204, 222, 238, 246, 286, 312, 318, 348, 364, 366, 374, 406, 408, 438, 444, 476, 492, 494, 518, 534, 546, 572, 574, 582, 598, 606, 624, 636, 638, 646, 654, 678, 696, 728, ...
If k^2 is the sum of 2 nonzero squares, (2*k)^(2*k) is. (2*k)^(2*k) = 2^(2*k) * k^(2*k) = (2^k)^2 * k^2 * k^(2*k-2) = (2^k)^2 * k^2 * (k^(k-1))^2. So if k^2 = a^2 + b^2, then (2*k)^(2*k) = (k^(k-1)*2^k*a)^2 + (k^(k-1)*2^k*b)^2. And if k^2 = a^2 + b^2 and k is not the sum of 2 nonzero squares, 2*k is not the sum of 2 nonzero squares. So 2 * A162592(n) appears in this sequence. Note that all terms appear as even numbers.
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..10000
EXAMPLE
30 is a term because 30 is not the sum of 2 nonzero squares and 30^30 = 8609344200000000000000^2 + 11479125600000000000000^2.
MATHEMATICA
Select[Range@ 120, SquaresR[2, #] == 0 && Resolve[Exists[{a, b}, Reduce[#^# == (a^2 + b^2), {a, b}, Integers], a > b > 0]] &] (* Michael De Vlieger, Jan 24 2016 *)
PROG
(PARI) isA000404(n) = {for( i=1, #n=factor(n)~%4, n[1, i]==3 && n[2, i]%2 && return); n && ( vecmin(n[1, ])==1 || (n[1, 1]==2 && n[2, 1]%2)); }
for(n=1, 1e3, if(isA000404(n^n) && !isA000404(n), print1(n, ", ")));
CROSSREFS
KEYWORD
nonn
AUTHOR
Altug Alkan, Jan 22 2016
STATUS
approved