OFFSET
1,3
COMMENTS
In other words, these are the products that are not in {2..2*n}.
Essentialy each unique product i*j that is not i+j for 1 <= i, j <= n is in A254671+1.
Conversely the number of distinct sums i+j with 1 <= i, j <= n which are not the product of two numbers between 1 and n is A060715.
a(n) < A263995(n).
EXAMPLE
a(3) = 2 because:
Prods = [1, 2, 3, 2, 4, 6, 3, 6, 9]
Sums = [2, 3, 4, 3, 4, 5, 4, 5, 6]
Items in Prods not in Sums : [1,9]
Total: 2.
a(4) = 4 because:
Prods = [1, 2, 3, 4, 2, 4, 6, 8, 3, 6, 9, 12, 4, 8, 12, 16]
Sums = [2, 3, 4, 5, 3, 4, 5, 6, 4, 5, 6, 7, 5, 6, 7, 8]
Items in Prods not in Sums: [1, 9, 12, 16]
Total: 4.
PROG
(Python)
def a(n):
P = {i * j for i in range(1, n+1) for j in range(1, n+1)}
return sum(1 for x in P if x > 2*n or x < 2)
print([a(n) for n in range(1, 54)])
(Python)
def A375109(n): return len({i*j for i in range(1, n+1) for j in range((n<<1)//i+1, i+1)})+1 # Chai Wah Wu, Aug 19 2024
(PARI) a(n) = #select(x->((x>2*n) || (x<2)), setbinop((x, y)->x*y, [1..n])); \\ Michel Marcus, Jul 30 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Darío Clavijo, Jul 30 2024
STATUS
approved