A104390 2-Smith numbers.

32, 42, 60, 70, 104, 152, 231, 315, 316, 322, 330, 342, 361, 406, 430, 450, 540, 602, 610, 612, 632, 703, 722, 812, 1016, 1027, 1029, 1108, 1162, 1190, 1246, 1261, 1304, 1314, 1316, 1351, 1406, 1470, 1510, 1603, 2013, 2054, 2065, 2070, 2071, 2106, 2114

Offset: 1

Author

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

Keywords

• nonn
• base

Examples

			32 is a 2-Smith number because the sum of the digits of its prime factors, i.e., Sp (32) = Sp(2*2*2*2*2)= 2 + 2 + 2 + 2 + 2 = 10, which is equal to twice the digit sum of 32, i.e., 2*S(32) = 2*(3 + 2) = 10.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 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, A104391.

Programs

Mathematica

d[n_]:=IntegerDigits[n]; tr[n_]:=Transpose[FactorInteger[n]]; Select[Range[2120],2Total[d[#]]==Total[d@tr[#][[1]]*tr[#][[2]],2]&] (* Jayanta Basu, Jun 04 2013 *)