A335286 - OEIS

%I #28 Jan 10 2022 15:06:32

%S 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,

%T 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,

%U 18,18,7,1,19,3,19,8,20,4,20,1,21,21,3,9,22,5,22,2

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

%H David A. Corneth, <a href="/A335286/b335286.txt">Table of n, a(n) for n = 1..10000</a>

%F Ordinal transform of A071364. - _Alois P. Heinz_, Jun 01 2020

%e 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.

%p p:= proc() 0 end:

%p a:= proc(n) option remember; local t; a(n-1); t:=

%p       (l-> mul(ithprime(i)^l[i][2], i=1..nops(l)

%p        ))(sort(ifactors(n)[2])); p(t):= p(t)+1

%p     end: a(0):=0:

%p seq(a(n), n=1..100);  # _Alois P. Heinz_, Jun 01 2020

%t A071364[n_] := If[n == 1, 1, With[{f = FactorInteger[n]}, Times @@ (Prime[Range[Length[f]]]^f[[All, 2]])]];

%t Module[{b}, b[_] = 0;

%t a[n_] := With[{t = A071364[n]}, b[t] = b[t] + 1]];

%t Array[a, 105] (* _Jean-François Alcover_, Jan 10 2022 *)

%o (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 }

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

%K nonn,easy

%O 1,3

%A _David A. Corneth_, May 30 2020