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A099637
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Numbers such that GCD[Sum,n] = A099635 and GCD[Sum,Product] = A099636 are not identical. Sum and Product here are the sum and product of all distinct prime factors of n.
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0
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84, 132, 168, 228, 234, 252, 260, 264, 276, 308, 336, 340, 372, 396, 456, 468, 504, 516, 520, 528, 532, 552, 558, 564, 580, 588, 616, 644, 672, 680, 684, 702, 708, 740, 744, 756, 792, 804, 820, 828, 836, 852, 855, 868, 884, 912, 936, 948, 996, 1008, 1012, 1032
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Of the first million integers, 75811 (of which 6300 are odd) belong to this sequence. - Robert G. Wilson v Nov 04 2004. - Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 04 2004
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EXAMPLE
| n=84: 84 is here because its factor-list={2,3,7} and sum=2+3+7=12,product=2.3.7=42,GCD[12,84]=12,GCD[12,42]=6. So 6 is not equal 12.
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MATHEMATICA
| <<NumberTheory`NumberTheoryFunctions` pf[x_] :=PrimeFactorList[x]; a=Table[Max[pf[w]], {w, 2, m}]; Table[GCD[Apply[Plus, pf[w]], Apply[Plus, pf[w]]], {w, 1, 100}]
PrimeFactors[n_Integer] := Flatten[ Table[ # [[1]], {1}] & /@ FactorInteger[n]]; fQ[n_] := Block[{pf = PrimeFactors[n]}, GCD[Plus @@ pf, n] == GCD[Plus @@ pf, Times @@ pf]]; Select[ Range[1039], ! fQ[ # ] &] (from Robert G. Wilson v Nov 04 2004)
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CROSSREFS
| Cf. A099634, A099635, A099636.
Sequence in context: A192322 A015708 A114822 * A143758 A101260 A141502
Adjacent sequences: A099634 A099635 A099636 * A099638 A099639 A099640
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Oct 28 2004
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 04 2004
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