A391044 Numbers k for which omega(k)*omega(k + 1)*omega(k + 2) = 2 where omega = A001221.

4, 5, 6, 8, 9, 11, 15, 16, 17, 23, 25, 27, 31, 47, 71, 79, 81, 107, 127, 191, 241, 431, 1151, 2591, 8191, 131071, 139967, 472391, 524287, 786431, 995327, 57395627, 63700991, 169869311, 2147483647, 4076863487, 10871635967, 2348273369087, 56358560858111, 79164837199871

Offset

1,1

Comments

Numbers k for which omega(k) + omega(k+1) + omega(k+2) = 4. - Robert Israel, Jan 01 2026

Links

Table of n, a(n) for n=1..40.

Maple

b:= 1: c:= 1: Res:= NULL: count:= 0:
for n from 4 while count < 34 do
  a:= b: b:= c: c:= NumberTheory:-NumberOfPrimeFactors(n, distinct);
  if a+b+c=4 then count:= count+1; Res:= Res, n-2; fi
od:
Res; # Robert Israel, Jan 01 2026

Mathematica

seq[lim_] := Module[{s = {}, om1 = PrimeNu[1], om2 = PrimeNu[2], om3}, Do[om3 = PrimeNu[k]; If[om1*om2*om3 == 2, AppendTo[s, k - 2]]; om1 = om2; om2 = om3, {k, 3, lim}]; s]; seq[10^6] (* Amiram Eldar, Jan 01 2026 *)

Prog

(Magma) [k: k in [1..10^6] | #PrimeDivisors(k)*#PrimeDivisors(k+1)*#PrimeDivisors(k+2) eq 2];

Crossrefs

Cf. A001221, A392184.

Sequence in context: A354834 A089585 A089253 * A047432 A095279 A030751

Adjacent sequences: A391041 A391042 A391043 * A391045 A391046 A391047

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jan 01 2026

Extensions

a(32)-a(37) from Amiram Eldar, Jan 01 2026

a(38)-a(40) from Jinyuan Wang, Jan 03 2026

Status

approved