cp's OEIS Frontend

Proof that this is a subsequence of squarefree numbers (A005117): Let's write A380459(n) = Product_{d|n} A276086(n/d)^A349394(d). Then suppose that we have a prime p such that p^e || n, with e > 1 (the maximal exponent e for which p^e divides n). We set d = p^e, and for that d, factor A276086(n/(p^e))^A349394(p^e) = A276086(n/(p^e))^(p^(e-1)) is contributed to the product A380459(n). But n/(p^e) is not divisible by p, so A020639(A276086(n/(p^e))) <= p as either p or some lesser prime q < p is the first prime missing from the factorization of n/(p^e) [see comments in A276086], so in the former case there will be a factor p^(p^(e-1)) [thus also p^p], and in the latter case a factor q^(p^(e-1)) [thus also q^q as p^(e-1) > q] present in the product, so in any such case the product will not be in A048103, and therefore each term must be squarefree.

The least terms k for which A001222(k) = 0, 1, 2, ..., are given in A380475.

See A380468 to find why each term must be squarefree.

After the initial 1 all terms here are even (thus in A039956) because as A276086(k) flips the parity of k, having more than one odd prime factor in k without a single 2 would make A380459(k) a multiple of 4, and thus outside of A048103.

For a similar reason, any term that is not a multiple of 3 may have at most 3 prime factors.