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

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

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. 36-37.

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 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).

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