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%I #18 Apr 03 2016 22:42:18
%S 20,22,24,26,28,30,33,36,39,40,42,44,46,48,50,55,60,62,63,64,66,68,69,
%T 70,77,80,82,84,86,88,90,93,96,99,110,121,130,132,143,150,154,156,165,
%U 169,170,176,187,190,198,200,202,204,206,208,220,222,224,226,228,231,240
%N Integers in A267509 such that (B0 + B1 + ... + Bm) is congruent to 0 mod m.
%C If Bi is congruent to 0 mod m for all i=1,2,...,m then the integer n = (Bm,...,B1,B0) is a member of this sequence if and only if n is a member of A267509.
%e 22 is a term, as f(x)=B0+B1x=2+2x=2*(1+x)=g(x)*h(x) with g(x)=2, h(x)=1+x, and neither g(x) nor h(x) is a unit in the ring of integers implies that f(x) is reducible over the ring of integers and 2+2=4=0 mod 1.
%e 121 is a term, as f(x)=B0+B1x+B2x^2=1+2x+1x^2=1+2x+x^2=(1+x)*(1+x)=g(x)*h(x) with g(x)=1+x=h(x) and neither g(x) nor h(x) is a unit in the ring of integers implies that f(x) is reducible over the ring of integers and 1+2+1=4=0 mod 2.
%t okQ[n_] := MatchQ[Factor[(id = IntegerDigits[n]).x^Range[lg = Length[id] - 1, 0, -1]][[0]], Times | Power] && Divisible[Total[id], lg]; Select[ Range[240], okQ] (* _Jean-François Alcover_, Feb 01 2016 *)
%Y Cf. A267509.
%K nonn,base
%O 1,1
%A _Abdul Gaffar Khan_, Jan 16 2016
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