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

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..1000

Shyam Sunder Gupta, Smith Numbers.

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

Example

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.

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 *)

Crossrefs

Cf. A006753.

Sequence in context: A284101 A303448 A251513 * A107618 A050945 A251458

Adjacent sequences: A103120 A103121 A103122 * A103124 A103125 A103126

Keyword

base,nonn

Author

Shyam Sunder Gupta, Mar 16 2005

Status

approved