Search: id:A051044
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%I A051044
%S A051044 1,1,3,5,15,27,89,165,585,1113,4097,7917,29927,58499,225585,444793,
%T A051044 1741521,3457027,13699699,27342421,109420549,219358315,884987529,
%U A051044 1780751883,7233519619,14600965705,59656252987,120742510607
%N A051044 Odd values of the PartitionsQ function A000009.
%C A051044 Weisstein comments: "The values of n for which a(n) is prime are 3, 4, 
               5, 7, 22, 70, 100, 495, 1247, 2072, 320397, ... (A035359), with no 
               others for n =< 3015000 (Weisstein, May 6, 2000). These values correspond 
               to 2, 2, 3, 5, 89, 29927, 444793, 602644050950309, ... (A051005). 
               It is not known if a(n) is infinitely often prime, but Gordon and 
               Ono (1997) proved that it is 'almost always' divisible by any given 
               power of 2 (1997)." Semiprime odd values of the PartitionsQ function 
               A000009 begin: a(4) = 15 = 3 * 5, a(10) = 4097 = 17 * 241, a(19) 
               = 27342421 = 389 * 70289, a(23) = 1780751883 = 3 * 593583961, a(27) 
               = 120742510607 = 31 * 3894919697. - Jonathan Vos Post (jvospost3(AT)gmail.com), 
               Jun 18 2005
%H A051044 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PartitionFunctionQCongruences.html">Link to a section of The World 
               of Mathematics.</a>
%F A051044 A000009(n) is odd iff n is of the form k*(3*k - 1)/2 or k*(3*k + 1)/2. 
               - Jonathan Vos Post (jvospost3(AT)gmail.com), Jun 18 2005
%F A051044 a(n) = A000009(A001318(n)). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Apr 22 2006
%Y A051044 Cf. A000009, A035359, A051005.
%Y A051044 Cf. A118303.
%Y A051044 Sequence in context: A053351 A146244 A146457 this_sequence A003536 A118173 
               A079450
%Y A051044 Adjacent sequences: A051041 A051042 A051043 this_sequence A051045 A051046 
               A051047
%K A051044 nonn
%O A051044 0,3
%A A051044 Eric Weisstein (eric(AT)weisstein.com)

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