OFFSET
1,2
COMMENTS
This sequence is a permutation of A355038.
This sequence is also a permutation of the exponentially odd numbers (A268335) multiplied by the square of their squarefree kernel (A007947).
a(n)/rad(a(n)) is a permutation of the squares.
a(n)/rad(a(n))^2 is a permutation of the exponentially odd numbers.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
FORMULA
Sum_{n>=1} 1/a(n) = Product_{p prime} (1 + 1/(p*(p^2-1))) = 1.2312911... (A065487).
EXAMPLE
8 = 2^3 is a term since the exponent of its prime factor 2 is 3 which is odd and larger than 1.
MATHEMATICA
Join[{1}, Select[Range[10^5], AllTrue[Last /@ FactorInteger[#], #1 > 1 && OddQ[#1] &] &]]
PROG
(Python)
from math import isqrt, prod
from sympy import factorint
def afind(N): # all terms up to limit N
cands = (n**2*prod(factorint(n**2)) for n in range(1, isqrt(N//2)+2))
return sorted(c for c in cands if c <= N)
print(afind(4*10**4)) # Michael S. Branicky, Jun 16 2022
CROSSREFS
A355038 in ascending order.
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jul 03 2020
STATUS
approved