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Search: id:A071145
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| A071145 |
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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 6 distinct prime factors and n is square-free. |
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| 72930, 106590, 190190, 222870, 335478, 397670, 620310, 836418, 844305, 884442, 1008678, 1195670, 1218945, 1247290, 1704794, 1761110, 1799798, 2086238, 2206022, 2328410, 2485830, 2496585, 2517258, 2863718, 2903538, 3024021
(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)=6, n is square-free.
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EXAMPLE
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n=pqrstw, p<q<r<s<t<w, primes, p+q+r+s+t+w=kt; n=106590=2.3.5.11.17.19; sum=2+3+5+11+17+19=57=3.19 (quotient=3) (Corrected Mar 06 2006.)
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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], 6]&& !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: A093212 A114258 A161730 this_sequence A023185 A105648 A122065
Adjacent sequences: A071142 A071143 A071144 this_sequence A071146 A071147 A071148
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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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