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A294278
Numbers k such that omega(k) > omega(k+1) (where omega(m) = A001221(m), the number of distinct primes dividing m).
8
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
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
KEYWORD
nonn,easy
AUTHOR
Rémy Sigrist, Oct 26 2017
STATUS
approved