A076762 2-apexes of omega: numbers k such that omega(k-2) < omega(k-1) < omega(k) > omega(k+1) > omega(k+2), where omega(m) = the number of distinct prime factors of m.

105, 165, 195, 315, 345, 399, 465, 1095, 1281, 1305, 1365, 1785, 1995, 2145, 2415, 2475, 2805, 3255, 3465, 3795, 3927, 4515, 4641, 4785, 4935, 5415, 5505, 5565, 5655, 5925, 5985, 6045, 6105, 6195, 6279, 6555, 6699, 6765, 6825, 7215, 7245, 7605, 7725

Offset

1,1

Comments

I call n a "k-apex" (or "apex of height k") of the arithmetical function f if n satisfies f(n-k) < ... < f(n-1) < f(n) > f(n+1) > .... > f(n+k).

Links

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

Formula

105 is a term since omega(105) = 3, omega(104) = omgea(106) = 2, and omega(103) = omega(107) = 1, so omega(103) < omega(104) < omega(105) > omega(106) > omega(107).

Mathematica

omega[n_] := Length[FactorInteger[n]]; Select[Range[4, 10^4], omega[ # - 2] < omega[ # - 1] < omega[ # ] > omega[ # + 1] > omega[ # + 2] &]

Crossrefs

Cf. A001222.

Sequence in context: A118678 A152940 A189936 * A036798 A119434 A091495

Adjacent sequences: A076759 A076760 A076761 * A076763 A076764 A076765

Keyword

nonn

Author

Joseph L. Pe, Nov 13 2002

Status

approved