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%I #8 Mar 30 2012 18:40:35
%S 8,10,12,20,26,28,45,58,63,68,76,81,82,92,99,106,115,116,129,146,159,
%T 165,171,172,188,195,202,212,213,218,225,236,255,259,261,268,273,279,
%U 298,309,325,339,343,351,362,375,387,395,399
%N Numbers n such that n-th octagonal number is 5-almost prime.
%C It is necessary but not sufficient that n must be prime (A000040), semiprime (A001358), 3-almost prime (A014612), or 4-almost prime (A014613).
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/OctagonalNumber.html">Octagonal Number.</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AlmostPrime.html">Almost Prime.</a>
%F n such that n*(3*n-2) has exactly five prime factors (with multiplicity). n such that A000567(n) is an element of A014614. n such that A001222(A000567(n)) = 5. n such that A001222(n) + A001222(3*n-2) = 5. n such that [(3*n-2)*(3*n-1)*(3*n)]/[(3*n-2)+(3*n-1)+(3*n)] is an element of A014614.
%e a(1) = 8 because OctagonalNumber(8) = Oct(8) = 8*(3*8-2) = 176 = 2^4 * 11 has exactly 5 prime factors (four are all equally 2; factors need not be distinct). Also, 176 = Oct(8) = Oct(Oct(2)), an iterated octagonal number. Also, 176 is a pengaonal number, hence an element of A046189 octagonal pentagonal numbers.
%e a(2) = 10 because Oct(10) = 10*(3*10-2) = 280 = 2^3 * 5 * 7 is 5-almost prime.
%e a(4) = 20 because Oct(20) = 20*(3*20-2) = 1160 = 2^3 * 5 * 29.
%e a(5) = 26 because Oct(26) = 26*(3*26-2) = 1976 = 2^3 * 13 * 19.
%e a(19) = 129 because Oct(129) = 129*(3*129-2) = 49665 = 3 * 5 * 7 * 11 * 43 is 5-almost prime (in this case, the 5 prime factors are distinct).
%Y Cf. A000040, A000567, A001222, A001358, A014612, A014613, A014614.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Feb 17 2006
%E 12, 63, 99 inserted and 117 removed by R. J. Mathar, Dec 22 2010
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