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

0,4

Links

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

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

Sequence in context: A108789 A091960 A162621 * A095394 A257682 A029928

Adjacent sequences: A180443 A180444 A180445 * A180447 A180448 A180449

Keyword

easy,nonn

Author

William A. Tedeschi, Sep 07 2010

Extensions

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

Status

approved