A097619 -id:A097619 - cp's OEIS frontend

A097620 Numbers having more prime factors than their neighbors together.

12, 16, 18, 24, 30, 32, 36, 40, 42, 48, 54, 60, 64, 72, 84, 88, 90, 96, 102, 108, 112, 120, 128, 132, 138, 140, 144, 150, 156, 160, 162, 168, 180, 192, 198, 200, 210, 216, 224, 228, 234, 240, 250, 252, 256, 264, 270, 272, 280, 282, 288, 294, 300, 304, 306, 308

Offset: 1

Reinhard Zumkeller, Aug 17 2004

nonn

			A001222(64) = A001222(2^6) = 6, A001222(64-1) = A001222(3*3*7) = 3, A001222(64+1) = A001222(5*13) = 2, and 6 > 3+2, therefore 64 is a term.

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Subsequence of A097619.

Cf. A001222.

from sympy import primeomega
def ok(n): return primeomega(n) > primeomega(n-1) + primeomega(n+1)
print([k for k in range(2, 309) if ok(k)]) # Michael S. Branicky, Dec 16 2021

{k: A001222(k) > A001222(k-1) + A001222(k+1)}. - Michael S. Branicky, Dec 16 2021

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

Original entry on oeis.org

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

Joseph L. Pe, Nov 13 2002

nonn

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

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

Cf. A001222, A097619.

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

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 *)

Edited by Robert Israel, Oct 28 2018

cp's OEIS Frontend

A097620 Numbers having more prime factors than their neighbors together.

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