A104391 3-Smith numbers.

402, 510, 700, 1113, 1131, 1311, 2006, 2022, 2130, 2211, 2240, 3102, 3111, 3204, 3210, 3220, 4031, 4300, 4410, 5310, 6004, 6100, 6300, 7031, 7120, 9000, 10034, 10125, 10206, 10251, 10304, 10413, 10521, 10612, 10800, 11033, 11111, 11114, 11116, 11121, 11141

Offset: 1

Author

Eric W. Weisstein, Mar 04 2005 and Shyam Sunder Gupta, Mar 11 2005

Keywords

• nonn
• base

Examples

			402 is a 3-Smith number because the sum of the digits of its prime factors, i.e., Sp(402) = Sp(2*3*67)= 2 + 3 + 6 + 7 = 18, which is equal to 3 times the digit sum of 402, i.e., 3*S(402) = 3*(4 + 0 + 2) = 18.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1500 from G. C. Greubel)
• Shyam Sunder Gupta, Smith numbers.
• Shyam Sunder Gupta, Smith Numbers, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 4, 127-157.
• Wayne L. McDaniel, The Existence of infinitely Many k-Smith numbers, Fibonacci Quarterly, Vol. 25, No. 1 (1987), pp. 76-80.

Crossrefs

Cf. A006753, A104390.

Programs

Mathematica

Select[Range[12000],Total[Flatten[IntegerDigits/@Table[#[[1]],{#[[2]]}]&/@ FactorInteger[#]]]/Total[IntegerDigits[#]]==3&] (* Harvey P. Dale, Feb 19 2013 *)