OFFSET
1,1
COMMENTS
If n is even, then n must have a prime factor of the form 4k+1. If n is odd, then all prime factors must be of the form 4k+1. - T. D. Noe, Oct 21 2013
The above is also a sufficient condition: the sequence consists exactly in even multiples of Pythagorean primes A002144, and products of such primes (A008846). - M. F. Hasler, Sep 02 2018
REFERENCES
G. H. Hardy and E. M. Wright, Theory of Numbers, Oxford, Sixth Edition, 2008, p. 395.
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
FORMULA
EXAMPLE
5^5 = 55^2 + 10^2.
10^10 = 99712^2 + 7584^2.
13^13 = 17106843^2 + 3198598^2.
17^17 = 28735037644^2 + 1240110271^2.
MATHEMATICA
t = {}; Do[f = FactorInteger[n]; p = Transpose[f][[1]]; If[EvenQ[n], If[MemberQ[Mod[p, 4], 1], AppendTo[t, n]], If[Union[Mod[p, 4]] == {1}, AppendTo[t, n]]], {n, 2, 200}]; t (* T. D. Noe, Oct 21 2013 *)
PROG
(PARI) select( is_A230486(n)={(n=factor(n)[, 1]%4) && if(n[1]==2, Set(n)[1]==1, Set(n)==[1])}, [1..200]) \\ M. F. Hasler, Sep 02 2018
(Python)
from itertools import count, islice
from sympy import primefactors
def A230486_gen(startvalue=2): # generator of terms >= startvalue
return filter(lambda n:all(p&3==1 for p in primefactors(n)) if n&1 else any(p&3==1 for p in primefactors(n)), count(max(startvalue, 2)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Alex Ratushnyak, Oct 20 2013
EXTENSIONS
Extended by T. D. Noe, Oct 21 2013
STATUS
approved