A358763 Numbers k for which bigomega(k) == 3 (mod 4).

8, 12, 18, 20, 27, 28, 30, 42, 44, 45, 50, 52, 63, 66, 68, 70, 75, 76, 78, 92, 98, 99, 102, 105, 110, 114, 116, 117, 124, 125, 128, 130, 138, 147, 148, 153, 154, 164, 165, 170, 171, 172, 174, 175, 182, 186, 188, 190, 192, 195, 207, 212, 222, 230, 231, 236, 238, 242, 244, 245, 246, 255, 258, 261, 266

Offset: 1

Author

Antti Karttunen, Nov 29 2022

Keywords

• nonn

Comments

Numbers k such that number of their prime factors (when counted with multiplicity, with A001222) is of the form 4n+3: 3, 7, 11, 15, 19, ..., A004767.

Equally, numbers k for which A349905(k) == 3 (mod 4).

Examples

			128 = 2^7 has 7 prime factors in total, and 7 is a number of the form 4n+3 (in A004767), therefore 128 is included in this sequence. Or equivalently, because A349905(128) = 5103 = 4*1275 + 3.
		

Links

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

Crossrefs

Cf. A001222, A003415, A003961, A004767, A010051, A010873, A349905, A358753 (characteristic function).

Setwise difference A026424 \ A358761.

Cf. also A358760, A358762.

Differs from its subsequences A014612, A212582 and A226527 for the first time at n=31, as a(31) = 128 is not present in those three sequences.

Programs

Maple

filter:= n -> numtheory:-bigomega(n) mod 4 = 3:
select(filter, [$1..1000]); # Robert Israel, Nov 29 2023

Mathematica

Select[Range[300],Mod[PrimeOmega[#],4]==3&] (* Harvey P. Dale, Apr 18 2025 *)

PARI

isA358763(n) = A358753(n);

Formula

{k | A010873(A349905(k)) = 3}.