OFFSET
1,1
COMMENTS
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
FORMULA
This sequence is { k = a^2*b^3 : a >= 1, b >= 1, omega(k) > 1, k mod 2 = 1 }.
Sum_{n>=1} 1/a(n) = 2*zeta(2)*zeta(3)/(3*zeta(6)) - 1/2 - Sum_{p prime} 1/(p*(p-1)) = (2/3) * A082695 - 1/2 - A136141 = 0.0225742... . - Amiram Eldar, May 28 2023
EXAMPLE
a(1) = 225 = 3^2 * 5^2, the smallest odd number with multiple distinct prime factors, each of which have multiplicity exceeding 1.
a(2) = 441 = 3^2 * 7^2,
a(3) = 675 = 3^3 * 5^2, etc.
MATHEMATICA
With[{nn = 20000}, Select[Union@ Flatten@ Table[a^2*b^3, {b, nn^(1/3)}, {a, Sqrt[nn/b^3]}], And[OddQ[#], ! PrimePowerQ[#]] &] ]
PROG
(PARI) isok(k) = (k>1) && (k%2) && ispowerful(k) && !isprimepower(k); \\ Michel Marcus, May 28 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael De Vlieger, May 21 2023
STATUS
approved