A279187 Maximal entry in row c of A279185, where c = n-th composite number A002808(n).

1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 4, 1, 4, 2, 6, 2, 1, 1, 4, 1, 2, 2, 6, 2, 1, 2, 4, 2, 10, 1, 6, 4, 1, 2, 6, 4, 2, 6, 3, 1, 4, 2, 1, 2, 4, 1, 10, 2, 2, 6, 4, 6, 4, 2, 1, 18, 4, 2, 1, 6, 3, 4, 2, 2, 10, 4, 11, 6, 1, 6, 4, 4, 1, 2, 2, 12, 6, 4, 6, 2, 6, 10, 3, 2

Offset: 1

Author

N. J. A. Sloane, Dec 14 2016

Keywords

• nonn

Comments

There are really two sequences that should be included if missing: the maximal entry in row c, and the LCM of the entries in row c.

a(n) and the LCM variant A256608(A002808(n)) are equal at least up to n<=1100. - R. J. Mathar, Dec 15 2016

Links

• R. J. Mathar, Table of n, a(n) for n = 1..1000
• Haifeng Xu, The largest cycles consist by the quadratic residues and Fermat primes, arXiv:1601.06509 [math.NT], 2016.

Crossrefs

Cf. A002808, A256608 (lcm of entries in row n), A279185, A279186 (max entry in row n).

Programs

Maple

A279187 := proc(n)
    A279186(A002808(n)) ;
end proc :
seq(A279187(n),n=1..180) ; # R. J. Mathar, Dec 15 2016

Mathematica

T[n_, k_] := Module[{g, y, r}, If[k == 0, Return[1]]; y = n; g = GCD[k, y]; While[g > 1, y = y/g; g = GCD[k, y]]; If[y == 1, Return[1]]; r = MultiplicativeOrder[k, y]; r = r/2^IntegerExponent[r, 2]; If[r == 1, Return[1]]; MultiplicativeOrder[2, r]]; Composite[n_] := FixedPoint[n + PrimePi[#] + 1&, n + PrimePi[n] + 1];
a[n_] := a[n] = With[{c = Composite[n]}, Table[T[c, k], {k, 0, c-1}] // Max ];
Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 1, 86}] (* Jean-François Alcover, Nov 27 2017, after Robert Israel *)