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A376745
Numbers that are not pentagonal pyramidal numbers.
2
2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71
OFFSET
1,1
COMMENTS
Complement of A002411. Numbers not of the form k^2*(k+1)/2.
LINKS
Eric Weisstein's World of Mathematics, Pentagonal Pyramidal Number
FORMULA
a(n) = n+m if 2n>m(m-1)(m+2) and a(n) = n+m-1 otherwise where m = floor((2n)^(1/3)).
MATHEMATICA
p=71; l=Floor[(2p)^(1/3)]; Complement[Range[p], Table[n^2 (n + 1)/2, {n, 0, l}]] (* James C. McMahon, Oct 07 2024 *)
PROG
(Python)
from sympy import integer_nthroot
def A376745(n): return n+(m:=integer_nthroot(k:=n<<1, 3)[0])-(k<=m*(m-1)*(m+2))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Chai Wah Wu, Oct 03 2024
STATUS
approved