OFFSET
1,1
COMMENTS
The sequence is inspired by problem 1, Junior Balkan Team Selection Tests - Romania 2023, Brasov, 13.04.2023, (see link).
If k >= 1 is a term, then for any m >= 1 the number m*k is also a term.
LINKS
Junior Balkan Team Selection Tests - Romania 2023, Problems
EXAMPLE
10 = 1 + 2 + 7 and (1 + 2)*(2 + 7)*(7 + 1) = 27*8 = 6^3, is a cube, so 10 is a term.
19 = 1 + 7 + 11 and (1 + 7)*(7 + 11)*(11 + 1) = 8*18*12 = 2^3*6^3 = 12^3, is a cube, so 19 is a term.
57 = 3 + 7 + 47 and (3 + 7)*(7 + 47)*(47 + 3) = 10*54*50 = 27*1000 = 30^3, is a cube. Also 57 = 3 + 21 + 33 and (3 + 21)*(21 + 33)*(33 + 3) = 24*54*36 = 36^2*36 = 36^3, is a cube.
PROG
(Magma) [n:n in [1..200]|exists(u){<a, b, n-a-b>:a in [1..n-2], b in [1..n-2]|a lt b and #{a, b, n-a-b} eq 3 and n-a-b gt 0 and IsPower((n-a)*(n-b)*(a+b), 3)}];
(Python)
from itertools import count, islice
from sympy import integer_nthroot
def A375323_gen(startvalue=1): # generator of terms >= startvalue
return (k for k in count(max(startvalue, 1)) if any(integer_nthroot(a*(a*(m:=b-k)+b*(m-k)+k**2)-b*k*m, 3)[1] for a in range(1, k//3) for b in range(a+1, k-a+1>>1)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Marius A. Burtea, Sep 15 2024
STATUS
approved