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Search: id:A071144
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| A071144 |
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Numbers n such that sum of distinct primes dividing n is divisible by the largest prime dividing n. Also n has exactly 5 distinct prime factors and n is square-free. |
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| 3570, 8970, 10626, 15015, 16530, 20706, 24738, 24882, 36890, 38130, 44330, 49938, 51051, 52170, 54834, 55986, 59570, 62985, 68370, 73554, 74613, 77330, 79458, 81770, 87290, 91266, 96162, 96866, 103730, 106314, 116466, 123234, 128570
(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; A001221(n)=5, n is square-free.
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EXAMPLE
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n=pqrst, p<q<r<s<t, primes, p+q+r+s+t=kt; n=8970=2.3.5.13.23: sum = 46 = 2.23.
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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], 5]&& !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: A083955 A104207 A107646 this_sequence A152217 A004932 A004952
Adjacent sequences: A071141 A071142 A071143 this_sequence A071145 A071146 A071147
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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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