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

1,2

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

Formula

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

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A033950, A000005, A036762, A281188.

Sequence in context: A162953 A235451 A348915 * A242424 A232271 A194277

Adjacent sequences: A039816 A039817 A039818 * A039820 A039821 A039822

Keyword

nonn

Author

N. J. A. Sloane.

Extensions

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

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

Status

approved