

A104167


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


1



1540, 1720, 2170, 2440, 5590, 6040, 7930, 8344, 8470, 8920, 23590, 24490, 25228, 29080, 31528, 31780, 33544, 34390, 35380, 39970, 40870, 42490, 42598, 43480, 44380, 45955, 46270, 46810, 46990, 47908, 48790, 49960, 51490, 51625, 52345, 52570, 53290, 57070
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OFFSET

1,1


COMMENTS

Numbers in the sequence must have a digital root of 1.
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


LINKS

Giovanni Resta, Table of n, a(n) for n = 1..1000
S. S. Gupta, Smith Numbers.
Sham Oltikar, and Keith Wayland, Construction of Smith Numbers, Mathematics Magazine, vol. 56(1), 1983, pp. 3637.
C. Rivera, Problem 108: Methods for generating Smith numbers, PrimePuzzles.Net.


EXAMPLE

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 sum of digits of 18920 is 1+8+9+2+0=20 and 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).


CROSSREFS

Cf. A006753, A004022.
Sequence in context: A202166 A133354 A283900 * A237400 A200429 A092717
Adjacent sequences: A104164 A104165 A104166 * A104168 A104169 A104170


KEYWORD

base,nonn


AUTHOR

Shyam Sunder Gupta, Mar 10 2005


STATUS

approved



