OFFSET
1,2
COMMENTS
T(n,k) is the number of numbers j with n prime factors, counted with multiplicity, such that j <= prime(k)^n.
EXAMPLE
T(2,3) = 9 because the third prime is 5 and 5^2 = 25 is the 9th semiprime.
MAPLE
T:= Matrix(12, 12):
with(priqueue);
for m from 1 to 12 do
initialize(pq);
insert([-2^m, [2$m]], pq);
k:= 0:
for count from 1 do
t:= extract(pq);
w:= t[2];
if nops(convert(w, set))=1 then
k:= k+1;
T[m, k]:= count;
if m+k = 13 then break fi;
fi;
p:= nextprime(w[-1]);
for i from m to 1 by -1 while w[i] = w[m] do
insert([t[1]*(p/w[-1])^(m+1-i), [op(w[1..i-1]), p$(m+1-i)]], pq);
od od od:
seq(seq(T[i, s-i], i=1..s-1), s=2..13)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Robert Israel, Sep 24 2024
STATUS
approved