A050225 1/3-Smith numbers.

6969, 19998, 36399, 39693, 66099, 69663, 69897, 89769, 99363, 99759, 109989, 118899, 181998, 191799, 199089, 297099, 306939, 333399, 336963, 339933, 363099, 396363, 397998, 399333, 399729, 588969, 606666, 606909, 639633, 660693, 666633

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

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.

Eric Weisstein's World of Mathematics, Smith Numbers.

Example

6969 is a 3^(-1) Smith number because the digit sum of 6969, i.e., S(6969) = 6 + 9 + 6 + 9 = 30, which is equal to 3 times the sum of the digits of its prime factors, i.e., 3*Sp(6969) = 3 * Sp(3 * 23 * 101) = 3 *( 3 + 2 + 3 + 1 + 0 + 1) = 30.

Mathematica

digSum[n_] := Plus @@ IntegerDigits[n]; thirdSmithQ[n_] := CompositeQ[n] && 3 * Plus @@ (Last@# * digSum[First@#] & /@ FactorInteger[n]) == digSum[n]; Select[Range[666633], thirdSmithQ] (* Amiram Eldar, Aug 23 2020 *)

Crossrefs

Cf. A006753, A050224.

Sequence in context: A263287 A234111 A184228 * A305718 A237237 A251651

Adjacent sequences: A050222 A050223 A050224 * A050226 A050227 A050228

Keyword

nonn,base

Author

Eric W. Weisstein

Extensions

More terms from Shyam Sunder Gupta, Mar 11 2005

Status

approved