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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.
9
1, 3, 4, 9, 10, 12, 14, 16, 22, 25, 26, 27, 30, 34, 35, 36, 38, 40, 42, 46, 48, 49, 55, 56, 58, 62, 64, 65, 66, 74, 75, 77, 78, 81, 82, 85, 86, 88, 90, 91, 94, 95, 100, 102, 104, 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
OFFSET
1,2
COMMENTS
A multiplicative semigroup: if m and n are in the sequence, then so is m*n.
Numbers such that the number of their prime factors (with multiplicity, A001222) and their 3-adic valuation (A007949) have the same parity.
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
LINKS
MATHEMATICA
Select[Range[200], EvenQ[PrimeOmega[#] - IntegerExponent[#, 3]] &] (* Paolo Xausa, Dec 17 2024 *)
PROG
(PARI) isA373586 = A373585;
CROSSREFS
Positions of even terms in A373149.
Cf. A000045, A001222, A007949, A064989, A113177, A373585 (characteristic function), A373587 (complement).
Subsequences: A374108, A374114.
Sequence in context: A276986 A283984 A283985 * A275893 A325196 A242661
KEYWORD
nonn,changed
AUTHOR
Antti Karttunen, Jun 12 2024
STATUS
approved