A216436 For g=A201557(n), define a(n) as the prime p|g such that G(g/p) is maximum, where G(k) = sigma(k)/(k*log(log(k))).

17, 17, 19, 19, 19, 19, 19, 23, 23, 31, 31, 31, 7, 7, 7, 7, 7, 37, 37, 41, 43, 43, 43, 43, 43, 43, 2, 43, 2, 43, 2, 47, 47, 47, 47, 47, 47, 2, 47, 2, 47, 2, 47, 2, 53, 61, 61, 61, 61, 61, 61, 5, 5, 5, 67, 71, 11, 11, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73, 73

Offset: 1

Author

Michel Marcus, Sep 10 2012

Keywords

• nonn

Comments

The ratio G(A201557(n)/p)/G(A201557(n)) is defined by Nicolas as the Gronwall quotient (A201557 = proper GA1 numbers).

Links

• Michel Marcus, Table of n, a(n) for n = 1..1000
• G. Caveney, J.-L. Nicolas and J. Sondow, On SA, CA, and GA numbers, Ramanujan J., 29 (2012), 359-384.
• J.-L. Nicolas, Table of proper GA1 numbers up to 10^60, 2011.
• J.-L. Nicolas, Computation of GA1 numbers, 2011.

Crossrefs

Cf. A000203, A201557, A197638.

Programs

Maple

# See link "Computation of GA1 numbers".

PARI

findq(i) = {f = factor(i); maxqu = 0.0; qmax = 0; for(iq=1, length(f~), qq = f[iq,1]; qu = g(i/qq)/g(i); if (qu > maxqu, maxqu = qu; qmax = qq;) ); return (qmax);} \\ for i in A201557

Formula

G(A201557(n)/a(n)) >= G(A201557(n)/q) if prime q|A201557(n).

Extensions

Definition simplified and formula supplied by Jonathan Sondow, Sep 11 2012