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A335286
n is the a(n)-th positive integer having its sequence of exponents in canonical prime factorization.
2
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
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
KEYWORD
nonn,easy
AUTHOR
David A. Corneth, May 30 2020
STATUS
approved