A147802 Least m coprime to 3 minimizing A007947(m*(3^n-m)).

1, 1, 2, 1, 1, 25, 139, 289, 31, 1, 16096, 49, 7424, 588665, 619115, 83521, 8000000, 1515625, 505620842, 17643776, 244140625, 5443635008

Offset: 1

Author

M. F. Hasler, Nov 13 2008

Keywords

• nonn
• hard
• more

Comments

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)).

Crossrefs

Cf. A007947, A143700 (analog for 2^n), A147300 (general case).

Programs

Mathematica

rad[n_] := Times @@ FactorInteger[n][[All, 1]];
a[n_] := MinimalBy[Select[Range[3^n - 2], CoprimeQ[#, 3] &], rad[# (3^n - #)] &][[1]];
Reap[Do[Print[n, " ", an = a[n]]; Sow[an], {n, 1, 16}]][[2, 1]] (* Jean-François Alcover, Mar 27 2020 *)

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)A007947((n-a)*b=a)); b; }

Extensions

a(17) from Jean-François Alcover, Mar 28 2020

a(18)-a(22) from Giovanni Resta, Mar 29 2020