A103125 4-Smith numbers.

2401, 5010, 7000, 10005, 10311, 10410, 10411, 11060, 11102, 11203, 12103, 13002, 13021, 13101, 14001, 14101, 14210, 20022, 20121, 20203, 20401, 21103, 21112, 21120, 21201, 22040, 22101, 22201, 23030, 30003, 30031, 30320, 31002, 31101

Offset: 1

Author

Shyam Sunder Gupta, Mar 16 2005

Keywords

• base
• nonn

Examples

			2401 is a 4-Smith number because the sum of the digits of its prime factors, i.e., Sp(2401) = Sp(7*7*7*7) = 7 + 7 + 7 + 7 = 28, which is equal to 4 times the digit sum of 2401, i.e., 4*S(2401) = 4*(2 + 4 + 0 + 1) = 28.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..600 from Harvey P. Dale)
• 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

sn4Q[n_]:=Module[{a=Total[Flatten[IntegerDigits/@(Table[First[#],{Last[ #]}]&/@FactorInteger[n])]],b=4Total[IntegerDigits[n]]},a==b] (* Harvey P. Dale, Oct 03 2011 *)