A376479 - OEIS

%I #6 Sep 27 2024 23:07:51

%S 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,

%T 1,8,90,551,2556,1688,788,39,1,9,114,1243,5138,18452,7089,2249,64,1,

%U 10,164,1763,15590,44329,126096,28893,6340,103,1,11,253,3112,24646,179313,361249,827901,115180,17526

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

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

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

%p T:= Matrix(12,12):

%p with(priqueue);

%p for m from 1 to 12 do

%p   initialize(pq);

%p   insert([-2^m, [2$m]],pq);

%p   k:= 0:

%p   for count from 1 do

%p     t:= extract(pq);

%p     w:= t[2];

%p     if nops(convert(w,set))=1 then

%p       k:= k+1;

%p       T[m,k]:= count;

%p       if m+k = 13 then break fi;

%p     fi;

%p     p:= nextprime(w[-1]);

%p     for i from m to 1 by -1 while w[i] = w[m] do

%p       insert([t[1]*(p/w[-1])^(m+1-i),[op(w[1..i-1]),p$(m+1-i)]],pq);

%p od od od:

%p seq(seq(T[i,s-i],i=1..s-1),s=2..13)

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

%K nonn,tabl

%O 1,2

%A _Robert Israel_, Sep 24 2024