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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.
9

%I #16 Jun 29 2024 13:30:45

%S 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 58,62,64,65,66,74,75,77,78,81,82,85,86,88,90,91,94,95,100,102,104,

%U 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 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 A multiplicative semigroup: if m and n are in the sequence, then so is m*n.

%C Numbers such that the number of their prime factors (with multiplicity, A001222) and their 3-adic valuation (A007949) have the same parity.

%C 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 Antti Karttunen, <a href="/A373586/b373586.txt">Table of n, a(n) for n = 1..10000</a>

%o (PARI) isA373586 = A373585;

%Y Positions of even terms in A373149.

%Y Cf. A000045, A001222, A007949, A064989, A113177, A373585 (characteristic function), A373587 (complement).

%Y Subsequences: A374108, A374114.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jun 12 2024