A050224 1/2-Smith numbers.
88, 169, 286, 484, 598, 682, 808, 844, 897, 961, 1339, 1573, 1599, 1878, 1986, 2266, 2488, 2626, 2662, 2743, 2938, 3193, 3289, 3751, 3887, 4084, 4444, 4642, 4738, 4804, 4972, 4976, 4983, 5566, 5665, 5764, 5797, 5863
Offset: 1
Examples
88 is a 2^(-1) Smith number because the digit sum of 88, i.e., S(88) = 8 + 8 = 16, which is equal to twice the sum of the digits of its prime factors, i.e., 2 * Sp (88) = 2 * Sp (11 * 2 * 2 * 2) = 2 * (1 + 1 + 2 + 2 + 2) = 16.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 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.
- Eric Weisstein's World of Mathematics, Smith Numbers
Programs
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Mathematica
snoQ[n_]:=Total[IntegerDigits[n]]==2Total[Flatten[IntegerDigits/@ Flatten[ Table[First[#],{Last[#]}]&/@FactorInteger[n]]]]; Select[Range[ 6000], snoQ] (* Harvey P. Dale, Oct 15 2011 *)
Extensions
More terms from Shyam Sunder Gupta, Mar 11 2005
Comments