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A180150 Numbers n such that n and n+2 are both divisible by exactly 4 primes (counted with multiplicity). 4
54, 88, 150, 196, 232, 248, 294, 306, 328, 340, 342, 348, 460, 488, 490, 568, 570, 664, 712, 738, 774, 850, 856, 858, 868, 870, 948, 1012, 1014, 1060, 1096, 1110, 1148, 1190, 1204, 1206, 1208, 1210, 1218, 1254, 1274, 1276, 1290, 1302, 1314, 1420, 1430, 1448 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

"Quadruprimes" or "4-almost primes" that keep that property when incremented by 2. This sequence is to 4 as 3 is to A180117, as A092207 is to 2, and as A001359 is to 1. That is, this sequence is the 4th 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

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

FORMULA

{m in A014613 and m+2 in A014613} = {m such that bigomega(m) = bigomega(m+2) = 4} = {m such that A001222(m) = A001222(m+2) = 4}.

EXAMPLE

a(1) = 54 because 54 = 2 * 3^3 is divisible by exactly 4 primes (counted with multiplicity), and so is 54+2 = 56 = 2^3 * 7.

PROG

(PARI) is(n)=bigomega(n)==4 && bigomega(n+2)==4 \\ Charles R Greathouse IV, Jan 31 2017

CROSSREFS

Cf. A000040, A001222, A001358, A014614, A033987, A101637, A114106 (number of 4-almost primes <= 10^n).

Sequence in context: A043185 A039362 A043965 * A096512 A243542 A290146

Adjacent sequences:  A180147 A180148 A180149 * A180151 A180152 A180153

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Aug 12 2010

EXTENSIONS

More terms from R. J. Mathar, Aug 13 2010

STATUS

approved

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Last modified November 17 19:33 EST 2017. Contains 294834 sequences.