Search: id:A071144
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%I A071144
%S A071144 3570,8970,10626,15015,16530,20706,24738,24882,36890,38130,44330,49938,
%T A071144 51051,52170,54834,55986,59570,62985,68370,73554,74613,77330,79458,
%U A071144 81770,87290,91266,96162,96866,103730,106314,116466,123234,128570
%N A071144 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.
%F A071144 A008472(n)/A006530(n) is integer; A001221(n)=5, n is square-free.
%e A071144 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.
%t A071144 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}]
%Y A071144 Cf. A008472, A006530, A000961, A025475, A037074, A071139-A071147.
%Y A071144 Sequence in context: A083955 A104207 A107646 this_sequence A152217 A004932 
               A004952
%Y A071144 Adjacent sequences: A071141 A071142 A071143 this_sequence A071145 A071146 
               A071147
%K A071144 nonn
%O A071144 1,1
%A A071144 Labos E. (labos(AT)ana.sote.hu), May 13 2002

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