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A050225 1/3-Smith 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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
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
Sequence in context: A263287 A234111 A184228 * A305718 A237237 A251651
KEYWORD
nonn,base
AUTHOR
EXTENSIONS
More terms from Shyam Sunder Gupta, Mar 11 2005
STATUS
approved

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Last modified February 26 12:39 EST 2024. Contains 370352 sequences. (Running on oeis4.)