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Search: id:A111751
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| A111751 |
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Numbers n such that P(3*n + 1) has exactly two distinct prime factors - where P(m) is the partition number. |
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| 2, 22, 25, 28, 37, 40, 60, 73, 78, 80, 129, 135, 158, 162, 215, 220, 228, 238, 269, 285, 315, 332, 344, 347, 355, 365, 366, 390, 397, 402, 439, 443, 470, 477, 533, 549, 653, 694, 710, 715, 716, 745, 765, 782, 822
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OFFSET
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1,1
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EXAMPLE
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If n=2 then P(3*n + 1) = 15 = 3 x 5 (two distinct prime factors), so the first term is 2.
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MAPLE
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with(combinat): with(numtheory): a:=proc(n) if nops(factorset(numbpart(3*n+1)))=2 then n else fi end: seq(a(n), n=1..300); (Deutsch)
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MATHEMATICA
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For[n = 1, n < 550, n++, If[Length[FactorInteger[PartitionsP[3*n + 1]]] == 2, Print[n]]] (Steinerberger)
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CROSSREFS
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Sequence in context: A080283 A080433 A022373 this_sequence A037416 A057871 A152243
Adjacent sequences: A111748 A111749 A111750 this_sequence A111752 A111753 A111754
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KEYWORD
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nonn
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AUTHOR
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Parthasarathy Nambi (PachaNambi(AT)yahoo.com), Nov 19 2005
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EXTENSIONS
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More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com) and Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 27 2006
More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 30 2006
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