A373767 Integers k such that the sum of the first k noncubes is a square.
3, 7, 15, 37, 69, 188, 254, 19274, 20798, 22380, 26439, 28219, 30057, 189067, 279203, 369162, 1517727, 1528134, 2964593, 3978491, 4645227, 4701433, 4757977, 4895880, 4953578, 5011614, 5062958, 7200291, 20845013, 51370845, 101900477, 135141272, 246185759, 358784011, 646164289
Offset: 1
Keywords
Examples
The 3 first noncubes add up to 2+3+4=9, a square. So 3 is a term.
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..64
Programs
-
PARI
nc(n) = n + sqrtnint(n + sqrtnint(n, 3), 3); \\ A007412 snc(n) = sum(k=1, n, nc(k)); \\ A109470 isok(k) = issquare(snc(k));
-
Python
from itertools import count, islice from sympy.ntheory.primetest import is_square def A373767_gen(): # generator of terms k, c = 0, 0 for i in count(1): for n in range(i**3+1,(i+1)**3): k += 1 c += n if is_square(c): yield k A373767_list = list(islice(A373767_gen(),20)) # Chai Wah Wu, Jun 18 2024
Extensions
a(14)-a(35) from Pontus von Brömssen, Jun 18 2024