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A176385 The smallest number which when multiplied by the n-th repunit gives a Smith number.

%I A176385 #4 Mar 31 2012 23:01:19
%S A176385 4,2,6,56,32,97,6,95,176,4,32,309,68,68,194,616,175,96,1540,4,816,14,
%T A176385 1540,95,840,32,5,437,50,10336,95,5,995,976,175,14,40,570,1976,995,
%U A176385 1400,294,1994,176,544,507,328,392,77,11020,18905,18050,9995,779,4,805,669
%N A176385 The smallest number which when multiplied by the n-th repunit gives a Smith number.
%C A176385 Smith numbers, A006753: the digits-sum equals the digits-sum of its prime factors.
%C A176385 Repunits: R(n)=(10^n-1)/9 = A002275(n).
%H A176385 Paul Weisenhorn, <a href="/A176385/b176385.txt">Table of n, a(n) for n = 1..70</a>
%e A176385 R(3)=111 multiplied by a(3)=6 yields z=666=2*3*3*37 = A006753(34): 6+6+6 = 2+3+3+3+7 = 18.
%p A176385 # digits-sum of primfactors of z=dsp(z)
%p A176385 for n from 2 to 70 do f(n):=1: test:=false:
%p A176385 while (f(n) < 420000) and (test=false) do
%p A176385 f(n):=f(n)+1: z:=f(n)*r(n): ds(z):=0:
%p A176385 dsp(z):=dsp(r(n))+dsp(f(n)):
%p A176385 while (z>0) do z:=iquo(z,10,'m'): ds(z):=ds(z)+m: end do:
%p A176385 if(ds(z)=dsp(z)) then test:=true: print(n,f(n)): end if:
%p A176385 end do: end do:
%K A176385 nonn,base
%O A176385 1,1
%A A176385 _Paul Weisenhorn_, Apr 16 2010, Apr 23 2010
%E A176385 Keyword:base added by _R. J. Mathar_, Apr 24 2010