A076764 n such that Omega(n-1) < Omega(n) < Omega(n+1), where Omega(m) = the number of prime factors of m, counting multiplicity.

62, 63, 74, 188, 194, 195, 207, 242, 255, 275, 278, 279, 314, 363, 374, 398, 399, 404, 422, 423, 455, 458, 483, 494, 495, 524, 539, 614, 615, 662, 663, 674, 692, 728, 734, 735, 747, 758, 759, 764, 782, 783, 854, 867, 890, 927, 935, 975, 998, 999

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

Omega(61) = 1 < Omega(62) = 2 < Omega(63) = 3, so 62 is a 1-apex of Omega.

Maple

Res:= NULL: a:= numtheory:-bigomega(1): b:= numtheory:-bigomega(2):
for n from 3 to 1001 do
  c:= numtheory:-bigomega(n);
  if a < b and b < c then Res:= Res, n-1 fi;
  a:= b; b:= c;
od:
Res; # Robert Israel, Oct 28 2018

Mathematica

Select[Range[3, 10^3], Omega[ # - 1] < Omega[ # ] < Omega[ # + 1] &]
Flatten[Position[Partition[PrimeOmega[Range[1000]], 3, 1], _?(Min[ Differences[ #]]>0&), {1}, Heads->False]]+1 (* Harvey P. Dale, Nov 28 2015 *)

Crossrefs

Cf. A001222, A097619.

Sequence in context: A296766 A003635 A188631 * A367090 A345496 A214251

Adjacent sequences: A076761 A076762 A076763 * A076765 A076766 A076767

Keyword

nonn

Author

Joseph L. Pe, Nov 13 2002

Extensions

Edited by Robert Israel, Oct 28 2018

Status

approved