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Search: id:A071141
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| A071141 |
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Sum of distinct primes dividing n is divisible by the largest prime dividing n. Also n is neither a prime, nor a true power of prime and n is square-free. Square-free solutions of A071140. |
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4
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| 30, 70, 286, 646, 1798, 3135, 3526, 3570, 6279, 7198, 8855, 8970, 10366, 10626, 10695, 11571, 15015, 16095, 16530, 17255, 17391, 20615, 20706, 20735, 20806, 23326, 24738, 24882, 26691, 28083, 31031, 36519, 36890, 38086, 38130, 41151
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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, n has at least 3 distinct prime factors and n is square-free.
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EXAMPLE
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n=286=2.11.13 has a form of 2pq, where p and q are twin primes; n=5414430=2.3.5.7.19.23.59, sum=2+3+5+7+19+23+59=118=2.59
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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]&&Greater[lf[n], 1]&& !Equal[amo[n], 1], 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: A064623 A112343 A131647 this_sequence A071312 A071142 A039517
Adjacent sequences: A071138 A071139 A071140 this_sequence A071142 A071143 A071144
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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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