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A071139
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Numbers n such that sum of distinct primes dividing n is divisible by largest prime dividing n.
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10
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2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 30, 31, 32, 37, 41, 43, 47, 49, 53, 59, 60, 61, 64, 67, 70, 71, 73, 79, 81, 83, 89, 90, 97, 101, 103, 107, 109, 113, 120, 121, 125, 127, 128, 131, 137, 139, 140, 149, 150, 151, 157, 163, 167, 169, 173, 179, 180
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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FORMULA
| A008472(n)/A006530(n) is integer.
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EXAMPLE
| Primes and prime powers are here. Various other composite solutions: 30=2.3.5, sum=10 is divisible by 5, quotient=2; 2181270=2.3.5.7.13.17.47, sum=47 is divisible by 47, quotient=1; if n is here then all multiples of n is also here which have no other prime-factors than n has. E.g. 286, 572, 3146 are equally suitable terms; if n=2pq, where p and q are twin primes then sum=p+q+2=2q is divisible by q, the largest prime factor so 2*A037074 is a subsequence.
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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], Print[{n, ba[n]}]], {n, 2, 1000000}]
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CROSSREFS
| Cf. A008472, A006530, A000961, A025475, A037074.
Sequence in context: A030230 A089352 A086486 * A046686 A137944 A087441
Adjacent sequences: A071136 A071137 A071138 * A071140 A071141 A071142
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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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