A338483 a(n) is the smallest number having n smaller numbers with the same number of divisors.

3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 35, 38, 39, 46, 51, 55, 57, 58, 62, 65, 69, 74, 77, 82, 85, 86, 87, 91, 93, 94, 95, 106, 111, 115, 118, 119, 122, 123, 125, 129, 133, 134, 141, 142, 143, 145, 146, 155, 158, 159, 161, 166, 177, 178, 183, 185, 187, 194, 201, 202, 203, 205, 206, 209, 213

Offset: 1

Author

Ivan N. Ianakiev, Oct 30 2020

Keywords

• nonn

Comments

Inspired by A047983.

Are there prime terms greater than 31?

Examples

			The smallest number having two smaller numbers (2 and 3) with the same number of divisors is 5, so a(2) is 5.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A007422, A030513, A047983.

Programs

Maple

N:= 500: # for terms before the first term > N
T:= map(numtheory:-tau, [$1..N]):
M:= max(T):
V:= Vector(M):
for n from 1 to N do
  v:= T[n];
  V[v]:= V[v]+1;
  if not assigned(R[V[v]]) then R[V[v]]:= n fi
od:
for nn from 1 while assigned(R[nn]) do od:
seq(R[i],i=2..nn-1); # Robert Israel, Oct 30 2020

Mathematica

f[n_]:=With[{tau=DivisorSigma[0,n]},Length[Select[Range[n-1],DivisorSigma[0,#]==tau&]]];t=Table[f[n],{n,1,300}]; a[n_]:=FirstPosition[t,n]; Rest[a/@Range[0,65]]//Flatten (* f(n) by Jean-François Alcover at A047983 *)

PARI

f(n) = {my(d=numdiv(n)); sum(k=1, n-1, (numdiv(k)==d))} \\ A047983
a(n) = my(k=1); while (f(k)!= n, k++); k; \\ Michel Marcus, Oct 30 2020

Formula

A047983(a(n)) = n. - Rémy Sigrist, Dec 06 2020