A103126 - OEIS

A103126

5-Smith numbers.

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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