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%I #19 Aug 11 2020 09:47:07
%S 1,1,2,1,1,25,139,289,31,1,16096,49,7424,588665,619115,83521,8000000,
%T 1515625,505620842,17643776,244140625,5443635008
%N Least m coprime to 3 minimizing A007947(m*(3^n-m)).
%C Related to the abc conjecture: Since m is coprime to 3, it is also coprime to 3^n and thus to 3^n-m. Thus A007947(m*(3^n-m)*3^n) = 3*A007947(m(3^n-m)).
%t rad[n_] := Times @@ FactorInteger[n][[All, 1]];
%t a[n_] := MinimalBy[Select[Range[3^n - 2], CoprimeQ[#, 3] &], rad[# (3^n - #)] &][[1]];
%t Reap[Do[Print[n, " ", an = a[n]]; Sow[an], {n, 1, 16}]][[2, 1]] (* _Jean-François Alcover_, Mar 27 2020 *)
%o (PARI) A147802(n, p=3) = {local(b, m=n=p^n); for(a=1, (n-1)\2, a%p || next; A007947(n-a)*A007947(a)<m || next; m=A007947((n-a)*b=a)); b; }
%Y Cf. A007947, A143700 (analog for 2^n), A147300 (general case).
%K nonn,hard,more
%O 1,3
%A _M. F. Hasler_, Nov 13 2008
%E a(17) from _Jean-François Alcover_, Mar 28 2020
%E a(18)-a(22) from _Giovanni Resta_, Mar 29 2020
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