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Search: id:A119028
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| A119028 |
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Numbers having at least 3 unique partitions into exactly 3 parts with the same product. |
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+0
3
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| 39, 45, 49, 53, 62, 64, 65, 70, 71, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84, 85, 87, 88, 89, 90, 91, 92, 93, 94, 95, 97, 98, 99, 100, 101, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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That is, numbers j such that there exist positive integers a1<=a2<=a3, b1<=b2<=b3, c1<=c2<=c3 (unique as triplets) with j = a1+a2+a3 = b1+b2+b3 = c1+c2+c3 and a1*a2*a3 = b1*b2*b3 = c1*c2*c3. The answer to a question raised by Tanya Khovanova, Jul 23 2006.
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EXAMPLE
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49=7+18+24 7*18*24=3024
49=8+14+27 8*14*27=3024
49=9+12+28 9*12*28=3024
or
49=9+20+20 9*20*20=3600
49=10+15+24 10*15*24=3600
49=12+12+25 12*12*25=3600
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MATHEMATICA
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pdt[lst_] := lst[[1]]*lst[[2]]*lst[[3]];
tanya[n_] := Max[Length /@ Split[Sort[pdt /@ Union[ Partition[Last /@ Flatten[ FindInstance[a + b + c == n && a >= b >= c > 0, {a, b, c}, Integers, (* failsafe *) PartitionsP@n]], 3]] ]]];
Select[ Range[4, 121], tanya@# >= 3 (*or strictly = ?*) &]
Select[Range[3, 121], Max[Length /@ Split[Sort[Times @@@ Partition[Last /@ Flatten[FindInstance[a + b + c == # && a >= b >= c > 0, {a, b, c}, Integers, (*cf A69905*) Round[ #^2/12]]], 3]]]] >= 3 &]
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CROSSREFS
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Cf. A069905.
Adjacent sequences: A119025 A119026 A119027 this_sequence A119029 A119030 A119031
Sequence in context: A050774 A041759 A061756 this_sequence A046512 A143746 A064399
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KEYWORD
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nonn
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AUTHOR
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Joseph Biberstine (jrbibers(AT)indiana.edu), Jul 23 2006, Aug 10 2006
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Jul 27 2006
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