A333996 Number of composite numbers in the triangular n X n multiplication table.
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
Examples
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*
Programs
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Mathematica
Array[Binomial[# + 1, 2] - PrimePi[#] - 1 &, 53] (* Michael De Vlieger, Nov 05 2020 *)
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PARI
a(n) = binomial(n+1, 2) - primepi(n)-1 \\ David A. Corneth, Sep 08 2020
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Python
from sympy import primepi def A333996(n): return (n*(n+1)>>1)-primepi(n)-1 # Chai Wah Wu, Oct 14 2023
Formula
a(n) = A256885(n) - 1. - Michel Marcus, Sep 09 2020
a(n+1) - a(n) = A014684(n+1). - Bill McEachen, Oct 30 2020
Comments