OFFSET
1,3
COMMENTS
The number of pairs (i,j) with 1 <= i <= j <= n and i*j composite. - Peter Kagey, Sep 24 2020
FORMULA
a(n) = A256885(n) - 1. - Michel Marcus, Sep 09 2020
a(n+1) - a(n) = A014684(n+1). - Bill McEachen, Oct 30 2020
EXAMPLE
There are a(7) = 23 composite numbers in the 7x7 triangular multiplication table with the hypotenuse being the Square numbers:
1 2 3 4* 5 6* 7
4* 6* 8* 10* 12* 14*
9* 12* 15* 18* 21*
16* 20* 24* 28*
25* 30* 35*
36* 42*
49*
MATHEMATICA
Array[Binomial[# + 1, 2] - PrimePi[#] - 1 &, 53] (* Michael De Vlieger, Nov 05 2020 *)
PROG
(PARI) a(n) = binomial(n+1, 2) - primepi(n)-1 \\ David A. Corneth, Sep 08 2020
(Python)
from sympy import primepi
def A333996(n): return (n*(n+1)>>1)-primepi(n)-1 # Chai Wah Wu, Oct 14 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Charles Kusniec, Sep 05 2020
STATUS
approved