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A104167 Numbers which when multiplied by any repunit prime Rp give a Smith number.

%I A104167 #30 Mar 14 2025 10:47:33
%S A104167 1540,1720,2170,2440,5590,6040,7930,8344,8470,8920,23590,24490,25228,
%T A104167 29080,31528,31780,33544,34390,35380,39970,40870,42490,42598,43480,
%U A104167 44380,45955,46270,46810,46990,47908,48790,49960,51490,51625,52345,52570,53290,57070
%N A104167 Numbers which when multiplied by any repunit prime Rp give a Smith number.
%C A104167 Numbers in the sequence must have a digital root of 1.
%C A104167 If the definition is modified, considering only repunits greater than 11, other numbers have the same property: 3304, 12070, 11080, 11620, 16030, 21340, 22330, 24130, 24220. - _Mauro Fiorentini_, Jul 16 2015
%H A104167 Giovanni Resta, <a href="/A104167/b104167.txt">Table of n, a(n) for n = 1..1000</a>
%H A104167 Shyam Sunder Gupta, <a href="http://www.shyamsundergupta.com/smith.htm">Smith Numbers</a>.
%H A104167 Shyam Sunder Gupta, <a href="https://doi.org/10.1007/978-981-97-2465-9_4">Smith Numbers</a>, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 4, 127-157. See also <a href="https://doi.org/10.1007/978-981-97-2465-9_11">Repunit Numbers</a>, Ch. 11, 327-352.
%H A104167 Sham Oltikar, and Keith Wayland, <a href="http://www.jstor.org/stable/2690265">Construction of Smith Numbers</a>, Mathematics Magazine, vol. 56(1), 1983, pp. 36-37.
%H A104167 Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_108.htm">Problem 108: Methods for generating Smith numbers</a>, PrimePuzzles.Net.
%e A104167 1720 is a number in the sequence because 1720*Rp is always a Smith number, where Rp is a Repunit prime. Let Rp=11, so 1720*11=18920, which is a Smith number as the sum of digits of 18920 is 1+8+9+2+0 = 20 and the sum of digits of prime factors of 18920 (i.e., 2*2*2*5*11*43) is also 20 (i.e., 2+2+2+5+1+1+4+3).
%Y A104167 Cf. A006753, A004022.
%K A104167 base,nonn
%O A104167 1,1
%A A104167 _Shyam Sunder Gupta_, Mar 10 2005