A103123 1/4-Smith numbers.

19899699, 36969999, 36999699, 39699969, 39999399, 39999993, 66699699, 66798798, 67967799, 67987986, 69759897, 69889389, 69966699, 69996993, 76668999, 79488798, 79866798, 85994799, 86686886, 89769759, 89866568

Offset: 1

Author

Shyam Sunder Gupta, Mar 16 2005

Keywords

• base
• nonn

Examples

			19899699 is a 4^(-1) Smith number because the digit sum of 19899699, i.e., S(19899699) = 1 + 9 + 8 + 9 + 9 + 6 + 9 + 9 = 60, which is equal to 4 times the sum of the digits of its prime factors, i.e., 4*Sp(19899699) = 4*Sp (3*2203*3011) = 4*(3 + 2 + 2 + 0 + 3 + 3 + 0 + 1 + 1) = 15.
		

Links

• Amiram Eldar, 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.
• Wayne L. McDaniel, The Existence of infinitely Many k-Smith numbers, Fibonacci Quarterly, Vol. 25, No. 1 (1987), pp. 76-80.

Crossrefs

Cf. A006753.

Programs

Mathematica

digSum[n_] := Plus @@ IntegerDigits[n]; qSmithQ[n_] := CompositeQ[n] && 4 * Plus @@ (Last@# * digSum[First@#] & /@ FactorInteger[n]) ==  digSum[n]; Select[Range[10^8], qSmithQ] (* Amiram Eldar, Aug 23 2020 *)