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Numbers k for which bigomega(k) == 3 (mod 4).
6

%I #15 Nov 29 2023 19:34:03

%S 8,12,18,20,27,28,30,42,44,45,50,52,63,66,68,70,75,76,78,92,98,99,102,

%T 105,110,114,116,117,124,125,128,130,138,147,148,153,154,164,165,170,

%U 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

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

%C 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.

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

%H Robert Israel, <a href="/A358763/b358763.txt">Table of n, a(n) for n = 1..10000</a>

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

%e 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.

%p filter:= n -> numtheory:-bigomega(n) mod 4 = 3:

%p select(filter, [$1..1000]); # _Robert Israel_, Nov 29 2023

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

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

%Y Setwise difference A026424 \ A358761.

%Y Cf. also A358760, A358762.

%Y 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.

%K nonn

%O 1,1

%A _Antti Karttunen_, Nov 29 2022