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A255585
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Composite numbers k such that Sum_{i=1..t-1} d(i+1)/d(i) is prime, where d(1), ..., d(t) are the divisors of k in ascending order.
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2
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50, 98, 108, 242, 338, 375, 578, 1029, 1058, 1458, 1922, 2738, 3072, 3362, 3993, 4418, 5618, 7442, 8978, 9216, 10658, 13778, 14739, 18818, 20402, 20577, 21218, 22898, 26985, 31250, 34322, 45602, 46875, 49298, 55778, 58564, 59858, 72962, 73167, 74498, 78732
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OFFSET
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1,1
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COMMENTS
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The corresponding primes are 11, 13, 17, 17, 19, 17, 23, 19, 29, 23, 37, 43, 31, 47, 23, 53, 59, 67, 73, 43, 79, 89, 29, 103, 107, 31, 109, 113, 31, 29, 137, ...
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LINKS
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EXAMPLE
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98 is in the sequence because the divisors of 98 are {1, 2, 7, 14, 49, 98} and 2/1 + 7/2 + 14/7 + 49/14 + 98/49 = 13 is prime.
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MATHEMATICA
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lst={}; Do[s=0; Do[s=s+Divisors[n][[i+1]]/Divisors[n][[i]], {i, 1, Length[Divisors[n]]-1}]; If[PrimeQ[s]&&!PrimeQ[n], AppendTo[lst, n]], {n, 80000}]; lst
compQ[n_]:=Module[{d=Divisors[n]}, CompositeQ[n]&&PrimeQ[Total[ Rest[d]/ Most[d]]]]; Select[Range[80000], compQ] (* Harvey P. Dale, Sep 03 2015 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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