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.

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

Author

Antti Karttunen, Jun 12 2024

Keywords

• nonn

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

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Positions of even terms in A373149.

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

Subsequences: A374108, A374114.

Programs

Mathematica

Select[Range[200], EvenQ[PrimeOmega[#] - IntegerExponent[#, 3]] &] (* Paolo Xausa, Dec 17 2024 *)

PARI

isA373586 = A373585;