A373587 Numbers k for which A373149(k) is odd, where A373149 is fully additive with a(2) = 1 and a(p) = prevprime(p) for odd primes p.

2, 5, 6, 7, 8, 11, 13, 15, 17, 18, 19, 20, 21, 23, 24, 28, 29, 31, 32, 33, 37, 39, 41, 43, 44, 45, 47, 50, 51, 52, 53, 54, 57, 59, 60, 61, 63, 67, 68, 69, 70, 71, 72, 73, 76, 79, 80, 83, 84, 87, 89, 92, 93, 96, 97, 98, 99, 101, 103, 107, 109, 110, 111, 112, 113, 116, 117, 123, 124, 125, 127, 128, 129, 130, 131, 132

Offset

1,1

Comments

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

Links

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

Formula

{k | A001222(k)+A007949(k) == 1 (mod 2)}.

Mathematica

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

Prog

(PARI) isA373587(n) = !A373585(n);

Crossrefs

Positions of odd terms in A373149, positions of 0's in A373585.

Cf. A001222, A007949, A373586 (complement).

Sequence in context: A122546 A258775 A275894 * A299635 A170944 A074940

Adjacent sequences: A373584 A373585 A373586 * A373588 A373589 A373590

Keyword

nonn,easy

Author

Antti Karttunen, Jun 13 2024

Status

approved