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

1,2

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

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

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

Adjacent sequences: A373583 A373584 A373585 * A373587 A373588 A373589

Keyword

nonn

Author

Antti Karttunen, Jun 12 2024

Status

approved