OFFSET
1,1
COMMENTS
The asymptotic density of the terms in this sequence within the powerful numbers is (3+sqrt(2))/7 = 0.6306019... = A380735 - 1. - Amiram Eldar, Nov 26 2025
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
FORMULA
Sum_{n>=1} 1/a(n) = zeta(2)*zeta(3)/(3*zeta(6)) = A082695 / 3. - Amiram Eldar, Nov 26 2025
a(n) = 4*A335851(n). - Amiram Eldar, Nov 29 2025
EXAMPLE
Table n, a(n) for select n:
n a(n)
---------------------------
1 4 = 2^2
2 8 = 2^3
3 16 = 2^4
4 32 = 2^5
5 36 = 2^2 * 3^2
6 64 = 2^6
7 72 = 2^3 * 3^2
8 100 = 2^2 * 5^2
9 108 = 2^2 * 3^3
10 128 = 2^7
12 196 = 2^2 * 7^2
30 900 = 2^2 * 3^2 * 5^2
MAPLE
q:= n-> is(min(ifactors(n)[2][.., 2])>1):
select(q, [2*i$i=1..1152])[]; # Alois P. Heinz, Nov 26 2025
MATHEMATICA
With[{nn = 2400}, Union@ Flatten@ Table[If[EvenQ[#], #, Nothing] &[a^2*b^3], {b, Surd[nn, 3]}, {a, Sqrt[nn/b^3] } ] ]
PROG
(PARI) isok(k) = !(k % 2) && ispowerful(k); \\ Amiram Eldar, Nov 26 2025
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Michael De Vlieger, Nov 25 2025
STATUS
approved
