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

1,1

Comments

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

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

Links

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

Example

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.

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:

Crossrefs

Sequence in context: A019105 A183399 A248250 * A155829 A181051 A299631

Adjacent sequences: A176382 A176383 A176384 * A176386 A176387 A176388

Keyword

nonn,base

Author

Paul Weisenhorn, Apr 16 2010, Apr 23 2010

Extensions

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

Status

approved