A390278 All positive numbers except those that are the product of an even number of distinct primes (including 1).

2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 16, 17, 18, 19, 20, 23, 24, 25, 27, 28, 29, 30, 31, 32, 36, 37, 40, 41, 42, 43, 44, 45, 47, 48, 49, 50, 52, 53, 54, 56, 59, 60, 61, 63, 64, 66, 67, 68, 70, 71, 72, 73, 75, 76, 78, 79, 80, 81, 83, 84, 88, 89, 90, 92, 96, 97, 98, 99, 100

Offset

1,1

Comments

Numbers that either contain a repeated prime factor, or else are built from an odd number of distinct primes. Compare A174891.

Links

Table of n, a(n) for n=1..69.

Formula

k is term <=> Moebius(k) <= 0.

Example

Since 210 = 2*3*5*7 is the product of an even number of distinct primes it is not in this sequence but is a term of A246716.

Maple

select(n -> numtheory:-mobius(n) <= 0, [seq(1..100)]);

Mathematica

Select[Range[100], MoebiusMu[#] <= 0 &] (* Amiram Eldar, Nov 03 2025 *)

Crossrefs

Cf. A008683, A030059 (subsequence), A013929 (subsequence), A000040 (subsequence), A332785 (subsequence), A246716, A174891, A353629.

Sequence in context: A284946 A285901 A246716 * A374473 A362618 A371782

Adjacent sequences: A390275 A390276 A390277 * A390279 A390280 A390281

Keyword

nonn

Author

Peter Luschny, Nov 02 2025

Status

approved