A026808 a(n) is the number of products P of distinct positive integers satisfying P <= n.

0, 1, 2, 3, 4, 7, 8, 11, 12, 15, 16, 21, 22, 25, 28, 31, 32, 37, 38, 43, 46, 49, 50, 59, 60, 63, 66, 71, 72, 81, 82, 87, 90, 93, 96, 105, 106, 109, 112, 121, 122, 131, 132, 137, 142, 145, 146, 159, 160, 165, 168, 173, 174, 183, 186, 195

Offset

1,3

Comments

The products must contain at least two integers. - Sean A. Irvine, Oct 13 2019

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Sean A. Irvine, Java program (github)

Example

a(6) = 7 because the possible products are 1*2, 1*3, 1*4, 1*5, 1*6, 2*3, and 1*2*3. - Sean A. Irvine, Oct 13 2019

Maple

N:= 200: # for a(1)..a(N)
with(queue):Q:= new():
V:= Vector(N):
for i from 1 to N/2 do
  for j from i+1 to N while i*j <= N do
    p:= i*j;
    V[p]:= V[p]+1;
    if p*(j+1) <= N then enqueue(Q, [i, j]) fi
od od:
while not empty(Q) do
  s:= dequeue(Q);
  p:= convert(s, `*`);
  for k from s[-1]+1 to N while p*k <= N do
     pp:= p*k;
     V[pp]:= V[pp]+1;
     if pp*(k+1) <= N then enqueue(Q, [op(s), k]) fi
  od;
od:
ListTools:-PartialSums(convert(V, list)); # Robert Israel, Dec 09 2020

Crossrefs

Partial sums of A254578.

Sequence in context: A343603 A285506 A188190 * A240767 A342028 A368402

Adjacent sequences: A026805 A026806 A026807 * A026809 A026810 A026811

Keyword

nonn

Author

Clark Kimberling

Status

approved