A299766 Greatest odd noncomposite divisor of n.

1, 1, 3, 1, 5, 3, 7, 1, 3, 5, 11, 3, 13, 7, 5, 1, 17, 3, 19, 5, 7, 11, 23, 3, 5, 13, 3, 7, 29, 5, 31, 1, 11, 17, 7, 3, 37, 19, 13, 5, 41, 7, 43, 11, 5, 23, 47, 3, 7, 5, 17, 13, 53, 3, 11, 7, 19, 29, 59, 5, 61, 31, 7, 1, 13, 11, 67, 17, 23, 7, 71, 3, 73, 37, 5, 19, 11, 13, 79, 5, 3, 41, 83, 7, 17, 43

Offset: 1

Author

Omar E. Pol, Mar 12 2018

Keywords

• nonn
• easy

Comments

The sequence can be constructed replacing the 2's with 1's in A006530.

Crossrefs

Cf. A000265 (odd part), A008578 (noncomposite numbers), A006005 (odd noncomposite numbers), A006530 (greatest noncomposite divisor).

Programs

Magma

[#f eq 1 select 1 else f[#f][1] where f is Factorization(2*n): n in [1..90]]; // Vincenzo Librandi, Mar 20 2018

Maple

A299766 := proc(n)
    local dvs ;
    dvs := sort(convert(numtheory[factorset](n) minus {2},list)) ;
    if nops(dvs) >= 1 then
        op(-1,dvs) ;
    else
        1;
    end if;
end proc: # R. J. Mathar, May 05 2018

Mathematica

Array[FactorInteger[#][[-1, 1]] /. 2 -> 1 &, 86] (* Michael De Vlieger, Mar 16 2018 *)
Table[Max[Select[Divisors[n],OddQ[#]&&!CompositeQ[#]&]],{n,100}] (* Harvey P. Dale, May 17 2024 *)

PARI

a(n) = my(m = n >> valuation(n, 2)); if (m==1, 1, vecmax(factor(m)[,1])); \\ Michel Marcus, Mar 15 2018

Formula

a(n) = A006530(A000265(n)). - Michel Marcus, Mar 15 2018

a(n) = 1 for n in A000079 (powers of 2). - Michel Marcus, Apr 14 2018