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%I #17 May 07 2017 15:16:00
%S 1,2,3,4,5,7,8,9,10,12,13,14,15,16,18,19,20,21,23,24,25,26,27,29,30,
%T 31,32,34,35,36,37,38,40,41,42,43,45,46,47,48,49,51,52,53,54,56,57,58,
%U 59,60,62,63,64,65,67,68,69,70,71,73,74,75,76,78,79,80,81,82,84,85,86
%N Numbers n such that n(n+1)(n+2)...(n+10) /(n+(n+1)+(n+2)+...+(n+10)) is a multiple of n.
%C Equals natural numbers minus '6,11,17,22,28,...' (= previous term +5,+6,+5,+6,...).
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 0, 0, 0, 0, 0, 1, -1).
%F From _Chai Wah Wu_, Dec 17 2016: (Start)
%F a(n) = a(n-1) + a(n-9) - a(n-10) for n > 10.
%F G.f.: x*(x^9 + x^8 + x^7 + x^6 + 2*x^5 + x^4 + x^3 + x^2 + x + 1)/(x^10 - x^9 - x + 1). (End)
%t nmnQ[n_]:=With[{c=n+Range[0,10]},Divisible[Times@@c/Total[c],n]]; Select[ Range[ 100],nmnQ] (* or *) LinearRecurrence[{1,0,0,0,0,0,0,0,1,-1},{1,2,3,4,5,7,8,9,10,12},80] (* _Harvey P. Dale_, May 07 2017 *)
%o (PARI) is(n)=factorback(vector(10,i,n+i))%(11*n+55)==0 \\ _Charles R Greathouse IV_, Aug 07 2016
%Y Cf. A032765-A032798.
%K nonn,easy
%O 1,2
%A _Patrick De Geest_, May 15 1998
%E Typo in definition corrected by _Zak Seidov_, Aug 06 2016
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