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Search: id:A071142
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| A071142 |
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Sum of distinct primes dividing n is divisible by the largest prime dividing n. Also n has exactly 3 distinct prime factors and n is square-free. |
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| 30, 70, 286, 646, 1798, 3526, 7198, 10366, 20806, 23326, 38086, 44998, 64798, 73726, 78406, 103966, 115198, 145798, 159046, 194686, 242206, 352798, 373246, 426886, 544966, 649798, 719998, 763846, 824326, 871198, 1312198, 1351366
(list; graph; listen)
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OFFSET
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1,1
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FORMULA
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A008472(n)/A006530(n) is integer; a(n)=2*A037074(n), n=2pq, where p and q=p+2 are twin prime pairs.
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EXAMPLE
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n=n=2.p.q=2p(p+2); sum=2+p+q=2+p+2+p=2q, where p and q are twin prime pairs.
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MATHEMATICA
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ffi[x_] := Flatten[FactorInteger[x]] lf[x_] := Length[FactorInteger[x]] ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}] sb[x_] := Apply[Plus, ba[x]] ma[x_] := Part[Reverse[Flatten[FactorInteger[x]]], 2] amo[x_] := Abs[MoebiusMu[x]] Do[s=sb[n]/ma[n]; If[IntegerQ[s]&&Equal[lf[n], 3]&& !Equal[amo[n], 0], Print[{n, ba[n]}]], {n, 2, 1000000}]
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CROSSREFS
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Cf. A008472, A006530, A000961, A025475, A037074, A071139-A071147.
Sequence in context: A131647 A071141 A071312 this_sequence A039517 A045560 A159219
Adjacent sequences: A071139 A071140 A071141 this_sequence A071143 A071144 A071145
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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), May 13 2002
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