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

Author

Shyam Sunder Gupta, Mar 10 2005

Keywords

• base
• nonn

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

Examples

			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).
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..1000
• Shyam Sunder Gupta, Smith Numbers.
• Shyam Sunder Gupta, Smith Numbers, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 4, 127-157. See also Repunit Numbers, Ch. 11, 327-352.
• Sham Oltikar, and Keith Wayland, Construction of Smith Numbers, Mathematics Magazine, vol. 56(1), 1983, pp. 36-37.
• Carlos Rivera, Problem 108: Methods for generating Smith numbers, PrimePuzzles.Net.

Crossrefs

Cf. A006753, A004022.