A094758 Least k <= n such that n*tau(k) = k*tau(n), where tau(n) is the number of divisors of n (A000005).

1, 1, 3, 4, 5, 3, 7, 8, 9, 5, 11, 8, 13, 7, 15, 16, 17, 9, 19, 20, 21, 11, 23, 9, 25, 13, 27, 28, 29, 15, 31, 32, 33, 17, 35, 36, 37, 19, 39, 40, 41, 21, 43, 44, 45, 23, 47, 48, 49, 25, 51, 52, 53, 27, 55, 56, 57, 29, 59, 40, 61, 31, 63, 64, 65, 33, 67, 68, 69, 35, 71, 72, 73, 37

Offset: 1

Author

Amarnath Murthy, May 30 2004

Keywords

• nonn

Examples

			6*tau(3) = 6*2 = 3*4 = 3*tau(6), hence a(6) = 3.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A095300 for n such that a(n) < n.

Cf. A000005, A094757, A094759.

Programs

Maple

A094758 := proc(n)
    for k from 1 to n do
        if n*numtheory[tau](k) = k*numtheory[tau](n) then
            return k;
        end if;
    end do:
end proc: # R. J. Mathar, Nov 15 2019

Mathematica

a[n_] := Module[{k = 1, r = DivisorSigma[0, n]/n}, While[DivisorSigma[0, k]/k != r, k++]; k]; Array[a, 100] (* Amiram Eldar, Aug 19 2019 *)

PARI

for(n=1,75,s=numdiv(n);k=1;while(n*numdiv(k)!=k*s,k++);print1(k,","));

Extensions

Edited and extended by Klaus Brockhaus, Jun 01 2004