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%I #11 Feb 05 2017 02:35:42
%S 4,5,6,9,10,11,13,15,17,21,22,29,34,43,47,49,51,55,57,61,67,69,71,73,
%T 82,87,89,91,101,103,106,107,109,115,121,127,129,141,142,151,159,166,
%U 169,177,181,187,191,197,201,205,217,223,227,241,251,262,269,274,277,283
%N Numbers n such that the n-th hexagonal number is a 3-almost prime.
%C There are no prime hexagonal numbers. The n-th hexagonal number A000384(n) = n*(2*n-1) is semiprime iff both n and 2*n-1 are prime iff A000384(n) is an element of A001358 iff n is an element of A005382.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HexagonalNumber.html">Hexagonal Number.</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AlmostPrime.html">Almost Prime.</a>
%F n such that hexagonal number A000384(n) is an element of A014612. n such that A001222(A000384(n)) = 3. n such that A001222(n*(2*n-1)) = 3.
%e a(1) = 4 because HexagonalNumber(4) = H(4) = 4*(2*4-1) = 28 = 2^2 * 7 is a 3-almost prime.
%e a(2) = 5 because H(5) = 5*(2*5-1) = 45 = 3^2 * 5 is a 3-almost prime.
%e a(3) = 6 because H(6) = 6*(2*6-1) = 66 = 2 * 3 * 11 is a 3-almost prime.
%p A000384 := proc(n) n*(2*n-1) ; end: isA014612 := proc(n) option remember ; RETURN( numtheory[bigomega](n) = 3) ; end: for n from 1 to 400 do if isA014612(A000384(n)) then printf("%d,",n) ; fi; od: # _R. J. Mathar_, Jan 27 2009
%Y Cf. A000384, A001222, A014612.
%K easy,nonn
%O 1,1
%A _Jonathan Vos Post_, Feb 14 2006
%E 151 to 177 inserted and extended by _R. J. Mathar_, Jan 27 2009
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