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A176385
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The smallest number which when multiplied by the n-th repunit gives a Smith number.
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1
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4, 2, 6, 56, 32, 97, 6, 95, 176, 4, 32, 309, 68, 68, 194, 616, 175, 96, 1540, 4, 816, 14, 1540, 95, 840, 32, 5, 437, 50, 10336, 95, 5, 995, 976, 175, 14, 40, 570, 1976, 995, 1400, 294, 1994, 176, 544, 507, 328, 392, 77, 11020, 18905, 18050, 9995, 779, 4, 805, 669
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OFFSET
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1,1
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COMMENTS
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Smith numbers, A006753: the digits-sum equals the digits-sum of its prime factors.
Repunits: R(n)=(10^n-1)/9 = A002275(n).
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LINKS
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EXAMPLE
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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.
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MAPLE
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# digits-sum of primfactors of z=dsp(z)
for n from 2 to 70 do f(n):=1: test:=false:
while (f(n) < 420000) and (test=false) do
f(n):=f(n)+1: z:=f(n)*r(n): ds(z):=0:
dsp(z):=dsp(r(n))+dsp(f(n)):
while (z>0) do z:=iquo(z, 10, 'm'): ds(z):=ds(z)+m: end do:
if(ds(z)=dsp(z)) then test:=true: print(n, f(n)): end if:
end do: end do:
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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