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A103126
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5-Smith numbers.
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2
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2030, 10203, 12110, 20210, 20310, 21004, 21010, 24000, 24010, 31010, 41001, 50010, 70000, 100004, 100012, 100210, 100310, 100320, 101020, 101041, 102022, 103200, 104010, 104101, 104110, 105020, 106001, 110020, 110202, 110212, 110400, 111013
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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LINKS
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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.
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EXAMPLE
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2030 is a 5-Smith number because the sum of the digits of its prime factors, i.e., Sp(2030) = Sp(2*5*7*29) = 2 + 5 + 7 + 2 + 9 = 25, which is equal to 5 times the digit sum of 2030, i.e., 5*S(2030) = 5*(2 + 0 + 3 + 0) = 25.
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MATHEMATICA
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digSum[n_] := Plus @@ IntegerDigits[n]; fiveSmithQ[n_] := CompositeQ[n] && Plus @@ (Last@# * digSum[First@#] & /@ FactorInteger[n]) == 5 *digSum[n]; Select[Range[10^5], fiveSmithQ] (* Amiram Eldar, Aug 23 2020 *)
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CROSSREFS
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Cf. A006753.
Sequence in context: A031543 A031723 A145721 * A045869 A098808 A212477
Adjacent sequences: A103123 A103124 A103125 * A103127 A103128 A103129
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KEYWORD
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base,nonn
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AUTHOR
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Shyam Sunder Gupta, Mar 16 2005
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STATUS
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approved
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