A180151 Numbers k such that k and k + 2 are both divisible by exactly five primes (counted with multiplicity).

270, 592, 700, 750, 918, 1168, 1240, 1638, 1648, 1672, 1710, 1750, 2070, 2310, 2392, 2548, 2550, 2608, 2728, 2860, 2862, 2896, 2898, 3184, 3330, 3568, 3630, 3822, 3848, 3850, 3942, 3976, 4230, 4264, 4648, 4662, 5070, 5080, 5236, 5238, 5390, 5550, 5560

Offset

1,1

Comments

"5-almost primes" that keep that property when incremented by 2. This sequence is to 5 as 4 is to A180150, as 3 is to A180117, as A092207 is to 2, and as A001359 is to 1. That is, this sequence is the 5th row of the infinite array A[k,n] = n-th natural number m such that m and m+2 are both divisible by exactly k primes (counted with multiplicity). The first row is the lesser of twin primes. The second row is the sequence such that m and m+2 are both semiprimes.

Links

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

Formula

{m in A014614 and m+2 in A014614} = {m such that bigomega(m) = bigomega(m+2) = 5} = {m such that A001222(m) = A001222(m+2) = 5}.

Example

a(1) = 270 because 270 = 2 * 3^3 * 5 is divisible by exactly 5 primes (counted with multiplicity), and so is 270+2 = 272 = 2^4 * 17.

Mathematica

f[n_] := Plus @@ (Last@# & /@ FactorInteger@n); fQ[n_] := f[n] == 5 == f[n + 2]; Select[ Range@ 10000, fQ] (* Robert G. Wilson v, Aug 15 2010 *)

Prog

(PARI) for(x=2, 10^4, if(bigomega(x)==5&&bigomega(x+2)==5, print1(x", "))) \\ Zak Seidov, Aug 12 2010

Crossrefs

Cf. A000040, A001222, A001358, A001359, A014614, A033987, A101637, A180117, A180150.

Sequence in context: A345173 A291789 A292766 * A278130 A206088 A029770

Adjacent sequences: A180148 A180149 A180150 * A180152 A180153 A180154

Keyword

easy,nonn

Author

Jonathan Vos Post, Aug 12 2010

Extensions

Corrected and extended by Zak Seidov and R. J. Mathar, Aug 12 2010

Status

approved