A335286 n is the a(n)-th positive integer having its sequence of exponents in canonical prime factorization.

1, 1, 2, 1, 3, 1, 4, 1, 2, 2, 5, 1, 6, 3, 4, 1, 7, 1, 8, 2, 5, 6, 9, 1, 3, 7, 2, 3, 10, 1, 11, 1, 8, 9, 10, 1, 12, 11, 12, 2, 13, 2, 14, 4, 5, 13, 15, 1, 4, 2, 14, 6, 16, 1, 15, 3, 16, 17, 17, 1, 18, 18, 7, 1, 19, 3, 19, 8, 20, 4, 20, 1, 21, 21, 3, 9, 22, 5, 22, 2

Offset: 1

Author

David A. Corneth, May 30 2020

Keywords

• nonn
• easy

Examples

			a(14) = 3 as 14 has prime signature [1, 1] and it's the third positive integer having that prime signature, after 6 and 10.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A046523, A064839, A071364, A120426, A254524.

Programs

Maple

p:= proc() 0 end:
a:= proc(n) option remember; local t; a(n-1); t:=
      (l-> mul(ithprime(i)^l[i][2], i=1..nops(l)
       ))(sort(ifactors(n)[2])); p(t):= p(t)+1
    end: a(0):=0:
seq(a(n), n=1..100);  # Alois P. Heinz, Jun 01 2020

Mathematica

A071364[n_] := If[n == 1, 1, With[{f = FactorInteger[n]}, Times @@ (Prime[Range[Length[f]]]^f[[All, 2]])]];
Module[{b}, b[_] = 0;
a[n_] := With[{t = A071364[n]}, b[t] = b[t] + 1]];
Array[a, 105] (* Jean-François Alcover, Jan 10 2022 *)

PARI

first(n) = { my(m = Map(), res = vector(n)); for(i = 1, n, c = factor(i)[,2]; if(mapisdefined(m, c), res[i] = mapget(m, c) + 1; mapput(m, c, res[i]) , res[i] = 1; mapput(m, c, 1) ) ); res }

Formula

Ordinal transform of A071364. - Alois P. Heinz, Jun 01 2020