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A071140
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Sum of distinct primes dividing n is divisible by largest prime dividing n; n is neither a prime, nor a true power of prime.
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4
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30, 60, 70, 90, 120, 140, 150, 180, 240, 270, 280, 286, 300, 350, 360, 450, 480, 490, 540, 560, 572, 600, 646, 700, 720, 750, 810, 900, 960, 980, 1080, 1120, 1144, 1200, 1292, 1350, 1400, 1440, 1500, 1620, 1750, 1798, 1800, 1920, 1960, 2160, 2240, 2250
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| a(n) are the numbers such that the difference between the largest and the smallest prime divisor equals the sum of the other prime distinct divisors. - Michel Lagneau, Nov 13 2011
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FORMULA
| A008472(n)/A006530(n) is integer and n has at least 3 distinct prime factors.
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EXAMPLE
| n=70=2.5.7 has a form of 2pq, where p and q are twin primes; n=3125=3.5.11.19, sum=3+5+11+19=38=2.19, divisible by 19.
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MATHEMATICA
| 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] Do[s=sb[n]/ma[n]; If[IntegerQ[s]&&Greater[s, 1], Print[{n, ba[n]}]], {n, 2, 1000000}]
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CROSSREFS
| Cf. A008472, A006530, A000961, A025475, A037074, A071139-A071147.
Sequence in context: A051488 A051283 A066031 * A074915 A056954 A050519
Adjacent sequences: A071137 A071138 A071139 * A071141 A071142 A071143
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), May 13 2002
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