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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.
0
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
1,2
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
Cf. A001222, A078843 (second column), A078844 (third column), A078845 (fourth column), A078846 (fifth column), A128301 (second row), A128302 (third row), A128304 (fourth row).
Sequence in context: A374738 A180165 A358349 * A142249 A274705 A257243
KEYWORD
nonn,tabl
AUTHOR
Robert Israel, Sep 24 2024
STATUS
approved