A365851 The number of divisors of the n-th practical number (A005153).

1, 2, 3, 4, 4, 6, 5, 6, 6, 8, 6, 8, 6, 9, 8, 8, 10, 8, 8, 12, 7, 8, 12, 8, 10, 12, 8, 12, 12, 9, 8, 12, 10, 16, 12, 8, 12, 12, 15, 12, 12, 12, 10, 16, 10, 18, 14, 9, 12, 12, 12, 10, 16, 16, 12, 12, 12, 12, 20, 18, 9, 12, 16, 16, 10, 12, 16, 18, 12, 18, 10, 12

Offset

1,2

Comments

a(n) = A000005(A005153(n)).

Links

Table of n, a(n) for n=1..72.

Example

A005153(1) = 1 and tau(1) = 1, so a(1) = 1.
A005153(2) = 2 and tau(2) = 2, so a(2) = 2.
A005153(3) = 4 and tau(4) = 3, so a(3) = 3.

Mathematica

f[p_, e_] := (p^(e + 1) - 1)/(p - 1); s[n_] := Module[{fct = FactorInteger[n], p, e}, p = fct[[;; , 1]]; e = fct[[;; , 2]]; If[Position[p/(1 + FoldList[Times, 1, f @@@ Most@ fct]), _?(# > 1 &)] == {}, Times @@ (e + 1), Nothing]]; s[1] = 1; Array[s, 320] (* Amiram Eldar, Oct 17 2023 *)

Prog

(Magma) sk:=func<n, k|&+[Divisors(n)[i]:i in [1..k]]>; ff:=func<n|forall{k:k in [2..#Divisors(n)]|sk(n, k-1) ge Divisors(n)[k]-1}>; a:=[]; for n in [1..400] do if ff(n) then Append(~a, #Divisors(n)); end if; end for; a;

Crossrefs

Cf. A000005, A005153.

Sequence in context: A178031 A008328 A298933 * A091860 A333995 A301764

Adjacent sequences: A365848 A365849 A365850 * A365852 A365853 A365854

Keyword

nonn

Author

Marius A. Burtea, Oct 17 2023

Status

approved