A376479 Array read by antidiagonals: T(n,k) is the index of prime(k)^n in the numbers with n prime factors, counted with multiplicity.

1, 2, 1, 3, 3, 1, 4, 9, 5, 1, 5, 17, 30, 8, 1, 6, 40, 82, 90, 14, 1, 7, 56, 328, 385, 269, 23, 1, 8, 90, 551, 2556, 1688, 788, 39, 1, 9, 114, 1243, 5138, 18452, 7089, 2249, 64, 1, 10, 164, 1763, 15590, 44329, 126096, 28893, 6340, 103, 1, 11, 253, 3112, 24646, 179313, 361249, 827901, 115180, 17526

Offset: 1

Author

Robert Israel, Sep 24 2024

Keywords

• nonn
• tabl

Comments

T(n,k) is the number of numbers j with n prime factors, counted with multiplicity, such that j <= prime(k)^n.

Examples

			T(2,3) = 9 because the third prime is 5 and 5^2 = 25 is the 9th semiprime.
		

Crossrefs

Cf. A001222, A078843 (second column), A078844 (third column), A078845 (fourth column), A078846 (fifth column), A128301 (second row), A128302 (third row), A128304 (fourth row).

Programs

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)