A180446 Number of non-pentagonal numbers <= n.

0, 0, 1, 2, 3, 3, 4, 5, 6, 7, 8, 9, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 63, 64, 65, 66

Offset: 0

Author

William A. Tedeschi, Sep 07 2010

Keywords

• easy
• nonn

Examples

			a(5) = 5 - floor((sqrt(24*5+1)+1)/6) = 3.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000

Programs

Mathematica

f[n_] := n - Floor[(Sqrt[24 n + 1] + 1)/6]; Array[f, 74, 0] (* Robert G. Wilson v, Sep 10 2010 *)
Accumulate[Table[If[IntegerQ[(1+Sqrt[1+24n])/6],0,1],{n,0,80}]]-1 (* Harvey P. Dale, May 22 2023 *)

Python

l = [n-floor((sqrt(24*n+1)+1)/6) for n in range(0,101)]

Python

from math import isqrt
def A180446(n): return n-(m:=isqrt((k:=n<<1)//3))-(k>m*(3*m+5)) # Chai Wah Wu, Nov 04 2024

Formula

a(n) = n - floor((sqrt(24n+1)+1)/6) = n - A180447(n).

Extensions

More terms from Robert G. Wilson v, Sep 10 2010