A039819 Number of divisors of n-th refactorable number (A033950(n)).

1, 2, 4, 3, 6, 6, 8, 9, 8, 8, 12, 12, 10, 12, 8, 12, 8, 12, 8, 12, 8, 8, 12, 18, 8, 12, 9, 12, 8, 20, 8, 18, 12, 18, 8, 8, 8, 12, 24, 12, 8, 16, 18, 8, 9, 12, 14, 18, 18, 8, 24, 8, 12, 24, 12, 8, 20, 12, 8, 8, 24, 18, 5, 8, 12, 16, 8, 24, 18, 12, 8, 30, 12, 8, 24, 12, 8, 8, 18, 12, 8, 24, 8

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

A number n is refactorable if the number of divisors of n divides n.

Links

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

Crossrefs

Cf. A033950, A000005, A036762, A281188.

Programs

Magma

v:=[ n: n in [1..900] | n mod NumberOfDivisors(n) eq 0 ]; [NumberOfDivisors(v[i]): i in [1..#v]]; // Marius A. Burtea, Jul 02 2019

Mathematica

fQ[n_] := Mod[n, DivisorSigma[0, n]] == 0; DivisorSigma[0, # ] & /@ Select[ Range[1000], fQ[ # ] &] (* Robert G. Wilson v *)

Formula

A033950(n)/a(n) = A036762(n).

a(n) = A000005(A033950(n)). - Omar E. Pol, Jan 17 2017

Extensions

More terms from Robert G. Wilson v, Oct 29 2005

Minor edits by Franklin T. Adams-Watters, Jan 17 2017