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

1,1

Comments

Inspired by A047983.

Are there prime terms greater than 31?

Links

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

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A000005, A007422, A030513, A047983.

Sequence in context: A132106 A242393 A210494 * A318871 A330225 A275938

Adjacent sequences: A338480 A338481 A338482 * A338484 A338485 A338486

Keyword

nonn

Author

Ivan N. Ianakiev, Oct 30 2020

Status

approved