

A050225


1/3Smith numbers.


3



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
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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 kSmith numbers, Fibonacci Quarterly, Vol. 25, No. 1 (1987), pp. 7680.
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



