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Search: id:A073763
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| A073763 |
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Least number of unrelated set belonging to these numbers is odd. |
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1
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| 24, 48, 96, 120, 168, 192, 240, 264, 312, 336, 384, 408, 456, 480, 528, 552, 600, 624, 672, 696, 744, 768, 816, 840, 888, 912, 960, 984, 1032, 1056, 1104, 1128, 1176, 1200, 1248, 1272, 1320, 1344, 1392, 1416, 1464, 1488, 1536, 1560, 1608, 1632, 1680, 1704
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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Solutions to Mod[A073758(x), 2]=1.
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EXAMPLE
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n=24: UnrelatedSet[24]={9, 10, 14, 15, 16, 18, 20, 21, 22}, Min=9, so 24 is here.In cases of all solutions (<50000) the odd number was always 9. This is not an accident. Primes are either divisors or primes to n. Thus a term here should be a composite odd number from A071904, whose first entry is 9; so next candidates are 15, 21, 25, 27... While 15 and 21 not [yet] found, prime powers 25 and 27 did arise.
Least odd unrelated number to 55440 is 25 and smallest unrelated (i.e. neither divisor, nor in RRS) to 3603600 is 27.
Question: can be a smallest odd unrelated number be other than a true power of odd prime?
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MATHEMATICA
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tn[x_] := Table[w, {w, 1, x}] di[x_] := Divisors[x] rrs[x_] := Flatten[Position[GCD[tn[x], x], 1]] nd[x_] := Complement[tn[x], di[x]] rs[x_] := Union[rrs[x], di[x]] urs[x_] := Complement[tn[x], rs[x]] Do[s=Min[urs[n]]; If[OddQ[s], Print[{n, s}]], {n, 1, 10000}]
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CROSSREFS
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Cf. A045763, A073757-A073762.
Cf. A071904.
Sequence in context: A054734 A029613 A083541 this_sequence A030021 A105844 A129837
Adjacent sequences: A073760 A073761 A073762 this_sequence A073764 A073765 A073766
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Aug 08 2002
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