OFFSET
1,1
COMMENTS
Every term is divisible by a cube.
If n and k are terms then n*k is a term if and only if gcd(n, k) = 1.
From Michael De Vlieger, Jan 19 2024: (Start)
Prime exponents of prime power factors p^m | k imply that k is a powerful number. Hence this sequence is a proper subset of A001694, and k is of the form a^2 * b^3.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
EXAMPLE
25015118625 = 3^5 * 5^3 * 7^7 is a term.
3125 = 5^5 and 3375 = 3^3 * 5^3 are terms but 3125*3375 is not a term.
MATHEMATICA
A369118Q[n_] := OddQ[n] && AllTrue[FactorInteger[n], OddQ[#] && PrimeQ[#]&, 2];
Select[Range[500000], A369118Q] (* Paolo Xausa, Jan 19 2024 *)
PROG
(SageMath)
def isA369118(n):
return (n > 1 and is_odd(n) and all(is_odd(f[1]) and is_prime(f[1])
for f in factor(n)))
print([n for n in range(1, 300000) if isA369118(n)])
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Jan 17 2024
STATUS
approved