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A103126 5-Smith numbers. 2
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)
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.

EXAMPLE

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.

MATHEMATICA

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 *)

CROSSREFS

Cf. A006753.

Sequence in context: A031543 A031723 A145721 * A045869 A098808 A212477

Adjacent sequences:  A103123 A103124 A103125 * A103127 A103128 A103129

KEYWORD

base,nonn

AUTHOR

Shyam Sunder Gupta, Mar 16 2005

STATUS

approved

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Last modified October 25 06:05 EDT 2020. Contains 338011 sequences. (Running on oeis4.)