Search: id:A108815
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%I A108815
%S A108815 7,9,11,12,14,17,18,19,21,25,28,29,30,33,34,38,41,42,43,52,57,66,67,70,
%T A108815 78,85,86,93,94,97,101,102,109,113,118,121,122,130,133,137,138,141,142,
%U A108815 145,148,158,163,172,173,177,181,190,201,202,205,211,213,214,217,218
%N A108815 Indices of triangular numbers which are products of 3 primes.
%C A108815 Indices of 3-almost prime triangular numbers.
%H A108815 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               TriangularNumber.html">Triangular Number.</a>
%H A108815 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               AlmostPrime.html">Almost Prime.</a>
%F A108815 {a(n)} = {k such that A001222(A000217(k)) = 3}. {a(n)} = {k such that 
               k*(k+1)/2 has exactly 3 prime factors, with multiplicity}. {a(n)} 
               = {k such that A000217(k) is an element of A014612}.
%F A108815 n such that n*(n+1)/2 is an element of A014612. n such that A000217(n) 
               is an element of A014612. n such that C(n+1, 2) is an element of 
               A014612.
%e A108815 a(1) = 7 because T(7) = TriangularNumber(7) = 7*(7+1)/2 = 28 = 2^2 * 
               7 is a 3-almost prime.
%e A108815 a(2) = 9 because T(9) = 9*(9+1)/2 = 45 = 3^2 * 5 is a 3-almost prime.
%e A108815 a(3) = 11 because T(11) = 11*(11+1)/2 = 66 = 2 * 3 * 11.
%e A108815 a(31) = 101 because T(101) = 101*(101+1)/2 = 5151 = 3 * 17 * 101.
%e A108815 a(49) = 173 because T(173) = 173*(173+1)/2 = 15051 = 3 * 29 * 173.
%t A108815 Select[Range[225], Plus @@ Last /@ FactorInteger[ #*(# + 1)/2] == 3 &] 
               (*Chandler*)
%Y A108815 Cf. A000217, A001222, A014612.
%Y A108815 Sequence in context: A112162 A058483 A162308 this_sequence A161992 A167377 
               A004169
%Y A108815 Adjacent sequences: A108812 A108813 A108814 this_sequence A108816 A108817 
               A108818
%K A108815 easy,nonn
%O A108815 1,1
%A A108815 Jonathan Vos Post (jvospost3(AT)gmail.com), Jul 10 2005
%E A108815 Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Jul 16 2005
%E A108815 Edited by N. J. A. Sloane (njas(AT)research.att.com), May 07 2007

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