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A130511 ABC conjecture: values of a in the list of "abc-hits".

%I A130511 #7 Oct 19 2023 22:31:57
%S A130511 1,5,1,1,1,32,4,3,1,1,2,7,13,81,1,100,32,5,169,1,27,1,49,81,1,1,25,
%T A130511 104,200,1,343,1,5,1,8,81,243,640,256,81,23,25,243,9,11,139,512,10,81,
%U A130511 1,125,1,25,192,1024,99,625,1,875,53,128,11,1024,25,459,128,648,1,1,512,7,1
%N A130511 ABC conjecture: values of a in the list of "abc-hits".
%H A130511 T. D. Noe, <a href="/A130511/b130511.txt">Table of n, a(n) for n=1..1269</a>
%o A130511 (Python)
%o A130511 from itertools import count, islice
%o A130511 from math import prod, gcd
%o A130511 from sympy import primefactors
%o A130511 def A130511_gen(): # generator of terms
%o A130511     for c in count(1):
%o A130511         pc = set(primefactors(c))
%o A130511         for a in range(1,(c>>1)+1):
%o A130511             b = c-a
%o A130511             if gcd(a,b)==1 and c>prod(set(primefactors(a))|set(primefactors(b))|pc):
%o A130511                 yield a
%o A130511 A130511_list = list(islice(A130511_gen(),30)) # _Chai Wah Wu_, Oct 19 2023
%Y A130511 Cf. A130510.
%K A130511 nonn
%O A130511 1,2
%A A130511 _T. D. Noe_, Jun 01 2007