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A373586 Numbers k for which A373149(k) is even, where A373149 is fully additive with a(2) = 1 and a(p) = prevprime(p) for odd primes p.

%I A373586 #24 Dec 17 2024 08:44:09
%S A373586 1,3,4,9,10,12,14,16,22,25,26,27,30,34,35,36,38,40,42,46,48,49,55,56,
%T A373586 58,62,64,65,66,74,75,77,78,81,82,85,86,88,90,91,94,95,100,102,104,
%U A373586 105,106,108,114,115,118,119,120,121,122,126,133,134,136,138,140,142,143,144,145,146,147,152,155,158,160,161
%N A373586 Numbers k for which A373149(k) is even, where A373149 is fully additive with a(2) = 1 and a(p) = prevprime(p) for odd primes p.
%C A373586 A multiplicative semigroup: if m and n are in the sequence, then so is m*n.
%C A373586 Numbers such that the number of their prime factors (with multiplicity, A001222) and their 3-adic valuation (A007949) have the same parity.
%C A373586 Also numbers k such that A113177(k) is even, where A113177 is fully additive with a(p) = Fibonacci(p), where Fibonacci(p) = A000045(p). - _Antti Karttunen_, Jun 29 2024
%H A373586 Antti Karttunen, <a href="/A373586/b373586.txt">Table of n, a(n) for n = 1..10000</a>
%t A373586 Select[Range[200], EvenQ[PrimeOmega[#] - IntegerExponent[#, 3]] &] (* _Paolo Xausa_, Dec 17 2024 *)
%o A373586 (PARI) isA373586 = A373585;
%Y A373586 Positions of even terms in A373149.
%Y A373586 Cf. A000045, A001222, A007949, A064989, A113177, A373585 (characteristic function), A373587 (complement).
%Y A373586 Subsequences: A374108, A374114.
%K A373586 nonn
%O A373586 1,2
%A A373586 _Antti Karttunen_, Jun 12 2024