A147804 Least m coprime to 7 minimizing A007947(m*(7^n-m)).

1, 1, 100, 1, 423, 28561, 3072, 124609, 119232

Offset: 1

Author

M. F. Hasler, Nov 13 2008

Keywords

• nonn
• more

Comments

The minima are given in A147799.

This is related to the abc conjecture: Since m is coprime to 7, it is also coprime to 7^n and thus to 7^n-m. Thus the squarefree kernel A007947(m*(7^n-m)*7^n) = 7*A007947(m(7^n-m)).

Crossrefs

Cf. A007947, A147799 (value of minima), A143700, A147802, A147803 (analog for 2^n, 3^n, 5^n), A147300 (analog for any number).

Programs

PARI

A147804(n,p=7)={my(b, m=3*n=p^n, t); for(a=1, n\2, a%p || next; m>2*(t=A007947(a)) || next; m>(t*=A007947(n-a)) || next; m=t; b=a); b; }

Extensions

Typo in title corrected by M. F. Hasler, Nov 17 2008