A174891 All positive numbers except those that are the product of an odd number of distinct primes.

1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 32, 33, 34, 35, 36, 38, 39, 40, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 68, 69, 72, 74, 75, 76, 77, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99

Offset

1,2

Comments

Original definition: "Row indices for nonzero elements in first column of A174888." Compare the first Mathematica program.

Numbers that either contain a repeated prime factor, or else are built from an even number of distinct primes (including 1). Compare A390278. - Peter Luschny, Nov 03 2025

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

k is term <=> Moebius(k) >= 0. - Peter Luschny, Nov 03 2025

Maple

select(n -> NumberTheory:-mu(n) >= 0, [$1..100]); # Robert Israel, Mar 08 2026

Mathematica

nn = 99;  (* Implementation of the original definition. *)
T = Table[A174888[[n, 1]], {n, 1, nn}]
A174891 = Flatten[Position[T, 1]]  (* Mats Granvik, Nov 03 2025 *)
Select[Range[99], MoebiusMu[#] >= 0 &]  (* Peter Luschny, Nov 03 2025 *)

Crossrefs

Cf. A008683, A013929 (subsequence), A030229 (subsequence), A174889, A174888, A018252, A390278.

Sequence in context: A077091 A340268 A340058 * A391939 A051035 A046349

Adjacent sequences: A174888 A174889 A174890 * A174892 A174893 A174894

Keyword

nonn

Author

Mats Granvik, Apr 01 2010

Extensions

New definition from Peter Luschny, Nov 03 2025

Status

approved