OFFSET
1,1
COMMENTS
Can be regarded as the cube version of A072357. Subsequence of A036537 (the number of divisors of any term is a power of 2). Also a subsequence of A048109.
Subsequence of A126706. - Michael De Vlieger, Feb 22 2023
The asymptotic density of this sequence is Sum_{p prime} d(p) = 0.074177741367259601921..., where d(p) = 1/(p^2*(p+1)*zeta(2)) is the density of the subset of terms that are divisible by p^3. - Amiram Eldar, Aug 01 2024
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
1608 = 2^3*201 is in this sequence (p = 2; m = 201 is odd and squarefree).
A001221(201) = 2, therefore 1608 has 2^(2+2) = 16 divisors.
MAPLE
filter:= proc(n) local F;
F:= sort(ifactors(n)[2][.., 2]);
nops(F) >= 2 and F[-1] = 3 and F[-2] = 1
end proc:
select(filter, [$1..1000]); # Robert Israel, Mar 01 2023
MATHEMATICA
Select[Range[1000], (e = Sort[FactorInteger[#][[;; , 2]]])[[-1]] == 3 && Length[e] > 1 && e[[-2]] == 1 &] (* Amiram Eldar, Feb 21 2023 *)
PROG
(PARI) isok(k) = if (k>1, my(f=factor(k), v=f[, 2], m); if (vecmax(v)==3, w=select(x->(x==3), v, 1); if (#w == 1, m = k/f[w[1], 1]^3; (m>1) && issquarefree(m)))); \\ Michel Marcus, Feb 21 2023
(Python)
from itertools import count, islice
from sympy import factorint
def A360793_gen(startvalue=1): # generator of terms >= startvalue
return filter(lambda n:len(f:=sorted(factorint(n).values(), reverse=True))>1 and f[0]==3 and f[1] == 1, count(max(startvalue, 1)))
CROSSREFS
KEYWORD
nonn
AUTHOR
David James Sycamore, Feb 21 2023
STATUS
approved