A375109 Number of distinct products i*j with 1 <= i, j <= n which are not the sum of two numbers between 1 and n.
1, 1, 2, 4, 6, 9, 14, 17, 22, 27, 35, 40, 50, 56, 64, 71, 85, 92, 109, 117, 128, 139, 159, 168, 182, 194, 208, 219, 245, 256, 285, 298, 314, 331, 349, 361, 396, 414, 433, 448, 486, 502, 542, 560, 580, 602, 646, 661, 691, 711, 737, 759, 809
Offset: 1
Examples
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.
Programs
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PARI
a(n) = #select(x->((x>2*n) || (x<2)), setbinop((x,y)->x*y, [1..n])); \\ Michel Marcus, Jul 30 2024
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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
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