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

1,1

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).

Links

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

Formula

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

Example

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.

Maple

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

Prog

(PARI) isA358763(n) = A358753(n);

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.

Sequence in context: A067537 A046339 A145784 * A014612 A226527 A212582

Adjacent sequences: A358760 A358761 A358762 * A358764 A358765 A358766

Keyword

nonn

Author

Antti Karttunen, Nov 29 2022

Status

approved