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A333996
Number of composite numbers in the triangular n X n multiplication table.
2
0, 1, 3, 7, 11, 17, 23, 31, 40, 50, 60, 72, 84, 98, 113, 129, 145, 163, 181, 201, 222, 244, 266, 290, 315, 341, 368, 396, 424, 454, 484, 516, 549, 583, 618, 654, 690, 728, 767, 807, 847, 889, 931, 975, 1020, 1066, 1112, 1160, 1209, 1259, 1310, 1362, 1414
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) = A000217(n) - A000720(n) - 1. - David A. Corneth, Sep 08 2020
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
Cf. A014684 (first differences), A333995, A108407, A000720, A000217, A256885, A334454.
Sequence in context: A134707 A047838 A188653 * A262502 A211076 A180452
KEYWORD
nonn,easy
AUTHOR
Charles Kusniec, Sep 05 2020
STATUS
approved