OFFSET
1,1
COMMENTS
The appearance of a number is determined by its prime signature.
No terms are squarefree, as the square root of the square part of a squarefree number is 1.
If the square part of k is a 4th power, other than 1, k appears.
Every positive integer k is the product of a unique subset S_k of the terms of A050376, which are arranged in array form in A329050 (primes in column 0, squares of primes in column 1, 4th powers of primes in column 2 and so on). k is in this sequence if and only if there is m >= 1 such that column m of A329050 contains a member of S_k, but column m - 1 does not.
LINKS
Eric Weisstein's World of Mathematics, Square part
EXAMPLE
4 is square and nontrivial (not 1), so 4 is in the sequence.
12 = 3 * 2^2 is nonsquare, but has square part 4, whose square root (2) is not in the sequence. So 12 is not in the sequence.
32 = 2 * 4^2 is nonsquare, and has square part 16, whose square root (4) is in the sequence. So 32 is in the sequence.
MAPLE
A337534 := proc(n)
option remember ;
if n =1 then
4;
else
for a from procname(n-1)+1 do
return a;
end if;
end do:
end if;
end proc:
seq(A337534(n), n=1..80) ; # R. J. Mathar, Feb 16 2021
MATHEMATICA
pow2Q[n_] := n == 2^IntegerExponent[n, 2]; Select[Range[625], ! pow2Q[1 + BitOr @@ (FactorInteger[#][[;; , 2]])] &] (* Amiram Eldar, Sep 18 2020 *)
CROSSREFS
Complement of A337533.
KEYWORD
nonn,easy
AUTHOR
Peter Munn, Aug 31 2020
STATUS
approved