A115166 Even numbers k such that k-2 and k+2 have the same number of distinct prime factors.

6, 8, 12, 16, 20, 22, 24, 26, 36, 38, 42, 46, 48, 50, 52, 54, 56, 60, 68, 70, 74, 78, 84, 90, 94, 96, 98, 102, 106, 110, 112, 114, 120, 128, 144, 146, 150, 152, 160, 162, 164, 172, 174, 184, 186, 188, 190, 194, 198, 204, 210, 214, 216, 232, 234, 236, 246, 252, 262

Offset

1,1

Links

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

Example

38 is in the sequence because 36 = 2^2 * 3^2 and 40 = 2^3 * 5.

Maple

with(numtheory): a:=proc(n) if nops(factorset(n-2))=nops(factorset(n+2)) then n else fi end: seq(a(2*n), n=2..133); # Emeric Deutsch, Mar 12 2006

Mathematica

Select[Range[2, 262, 2], PrimeNu[# - 2] == PrimeNu[# + 2] &] (* Amiram Eldar, Feb 18 2020 *)
Select[Mean/@SequencePosition[PrimeNu[Range[300]], {x_, _, _, _, x_}], EvenQ] (* Harvey P. Dale, Oct 11 2023 *)

Prog

(PARI) g(n) = forstep(x=4, n, 2, p1=omega(x-2); p2=omega(x+2); if(p1==p2, print(x", ")))
(Magma) [k:k in [4.. 270 by 2]| #PrimeDivisors(k-2) eq #PrimeDivisors(k+2)]; // Marius A. Burtea, Feb 18 2020

Crossrefs

Cf. A001221.

Subsequence of A005843.

Sequence in context: A177085 A338370 A194409 * A050992 A372011 A090259

Adjacent sequences: A115163 A115164 A115165 * A115167 A115168 A115169

Keyword

easy,nonn

Author

Cino Hilliard, Mar 03 2006

Status

approved