

A076760


3apexes of Omega: n such that Omega(n3) < Omega(n2)< Omega(n1) < Omega(n) > Omega(n+1) > Omega(n+2) > Omega(n+3), where Omega(m) = the number of prime factors of m, counting multiplicity.


0



1376, 6656, 9424, 12104, 18656, 19376, 29224, 30304, 40976, 41504, 41824, 44864, 51624, 57784, 59224, 61984, 66520, 70300, 70624, 70736, 72064, 74920, 82160, 87296, 93500, 94424
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

I call n a "kapex" (or "apex of height k") of the arithmetical function f if n satisfies f(nk) < ... < f(n1) < f(n) > f(n+1) > .... > f(n+k).


LINKS

Table of n, a(n) for n=1..26.


EXAMPLE

Omega(1373) = 1 < Omega(1374) = 3 < Omega(1375) = 4 < Omega(1376)= 6 > Omega(1377) = 5 > Omega(1378) = 3 > Omega(1379) = 2, so 1376 is a 3apex of Omega.


MATHEMATICA

Omega[n_] := Apply[Plus, Transpose[FactorInteger[n]][[2]]]; Select[Range[5, 10^5], Omega[ #  3] < Omega[ #  2] < Omega[ #  1] < Omega[ # ] > Omega[ # + 1] > Omega[ # + 2] > Omega[ # + 3] &]


CROSSREFS

Cf. A001222.
Sequence in context: A206340 A056087 A122692 * A283231 A283790 A323815
Adjacent sequences: A076757 A076758 A076759 * A076761 A076762 A076763


KEYWORD

nonn


AUTHOR

Joseph L. Pe, Nov 13 2002


STATUS

approved



