A294278 Numbers k such that omega(k) > omega(k+1) (where omega(m) = A001221(m), the number of distinct primes dividing m).

6, 10, 12, 15, 18, 22, 24, 26, 28, 30, 36, 40, 42, 46, 48, 52, 58, 60, 63, 66, 70, 72, 78, 80, 82, 84, 88, 90, 96, 100, 102, 105, 106, 108, 110, 112, 114, 120, 124, 126, 130, 132, 136, 138, 140, 148, 150, 154, 156, 162, 165, 166, 168, 170, 172, 174, 178, 180

Offset

1,1

Comments

The asymptotic density of this sequence is 1/2 (Erdős, 1936). - Amiram Eldar, Sep 17 2024

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Paul Erdős, On a problem of Chowla and some related problems, Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 32, No. 4 (1936), pp. 530-540; alternative link.

Example

omega(1) = 0 < omega(2) = 1, hence 1 does not belong to this sequence.
omega(4) = 1 = omega(5) = 1, hence 4 does not belong to this sequence.
omega(6) = 2 > omega(7) = 1, hence 6 belongs to this sequence.

Mathematica

Position[Differences[Array[PrimeNu, 200]], _?(# < 0 &)] // Flatten (* Amiram Eldar, Sep 17 2024 *)

Prog

(PARI) for (n=1, 180, if (omega(n) > omega(n+1), print1(n ", ")))

Crossrefs

Cf. A001221, A006049, A294277.

Sequence in context: A279550 A362754 A143958 * A373677 A297366 A378616

Adjacent sequences: A294275 A294276 A294277 * A294279 A294280 A294281

Keyword

nonn,easy

Author

Rémy Sigrist, Oct 26 2017

Status

approved