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

1,3

Links

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

Formula

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

Example

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.

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 *)

Prog

(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 }

Crossrefs

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

Sequence in context: A363943 A241919 A286469 * A064839 A347103 A255810

Adjacent sequences: A335283 A335284 A335285 * A335287 A335288 A335289

Keyword

nonn,easy

Author

David A. Corneth, May 30 2020

Status

approved