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A051044
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Odd values of the PartitionsQ function A000009.
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3
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1, 1, 3, 5, 15, 27, 89, 165, 585, 1113, 4097, 7917, 29927, 58499, 225585, 444793, 1741521, 3457027, 13699699, 27342421, 109420549, 219358315, 884987529, 1780751883, 7233519619, 14600965705, 59656252987, 120742510607
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| A000009(n) is odd iff n is of the form k*(3*k - 1)/2 or k*(3*k + 1)/2. - Jonathan Vos Post, Jun 18 2005
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, Jun 18 2005
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LINKS
| Eric Weisstein's World of Mathematics, Partition Function Q Congruences
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FORMULA
| a(n) = A000009(A001318(n)). - Reinhard Zumkeller, Apr 22 2006
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CROSSREFS
| Cf. A000009, A035359, A051005, A118303.
Sequence in context: A053351 A146244 A146457 * A003536 A118173 A079450
Adjacent sequences: A051041 A051042 A051043 * A051045 A051046 A051047
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KEYWORD
| nonn
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AUTHOR
| Eric Weisstein (eric(AT)weisstein.com)
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