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

Offset: 1

Author

Shyam Sunder Gupta, Mar 16 2005

Keywords

• base
• nonn

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Shyam Sunder Gupta, Smith Numbers.
• Shyam Sunder Gupta, Smith Numbers, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 4, 127-157.
• Wayne L. McDaniel, The Existence of infinitely Many k-Smith numbers, Fibonacci Quarterly, Vol. 25, No. 1 (1987), pp. 76-80.

Crossrefs

Cf. A006753.

Programs

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 *)