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A377721
Numbers that are not of the form k(k+1)(2k+1)/6 + k.
1
1, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72
OFFSET
1,2
COMMENTS
Complement of A145066. Numbers that are not of the form A000330(k)+k.
FORMULA
a(n) = n+m if n > m(m+1)(2m+1)/6 and a(n) = n+m-1 otherwise where m = floor((3n)^(1/3)).
a(n) = A074279(n)+n-1.
PROG
(Python)
from sympy import integer_nthroot
def A377721(n): return n+(m:=integer_nthroot(3*n, 3)[0])-(6*n<=m*(m+1)*((m<<1)+1))
CROSSREFS
KEYWORD
nonn
AUTHOR
Chai Wah Wu, Nov 04 2024
STATUS
approved