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

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

Offset: 1

Author

Paul Weisenhorn, Apr 16 2010, Apr 23 2010

Keywords

• nonn
• base

Comments

Smith numbers, A006753: the digits-sum equals the digits-sum of its prime factors.

Repunits: R(n)=(10^n-1)/9 = A002275(n).

Examples

			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.
		

Links

• Paul Weisenhorn, Table of n, a(n) for n = 1..70

Programs

Maple

# 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:

Extensions

Keyword:base added by R. J. Mathar, Apr 24 2010