

A180151


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


2



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
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OFFSET

1,1


COMMENTS

"5almost 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] = nth 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



