A174460 Smith numbers of order 2.
56, 58, 810, 822, 1075, 1519, 1752, 2145, 2227, 2260, 2483, 2618, 2620, 3078, 3576, 3653, 3962, 4336, 4823, 4974, 5216, 5242, 5386, 5636, 5719, 5762, 5935, 5998, 6220, 6424, 6622, 6845, 7015, 7251, 7339, 7705, 7756, 8460, 9254, 9303, 9355, 10481, 10626, 10659
Offset: 1
Examples
a(2) = 58 = 2*29 is a Smith number of order 2 because 5^2 + 8^2 = 2^2 + 2^2 + 9^2 = 89.
Links
- Ely Golden and Donovan Johnson, Table of n, a(n) for n = 1..10000 (terms 1 to 1000 by Donovan Johnson)
- Patrick Costello, A new largest Smith number, Fibonacci Quarterly 40(4) (2002), 369-371.
- Underwood Dudley, Smith numbers, Mathematics Magazine 67(1) (1994), 62-65.
- Ely Golden, Smith number sequence generator optimized for order 2.
- S. S. Gupta, Smith Numbers, Mathematical Spectrum 37(1) (2004/5), 27-29.
- S. S. Gupta, Smith Numbers.
- Eric Weisstein's World of Mathematics, Smith number.
- Wikipedia, Smith number.
- A. Wilansky, Smith Numbers, Two-Year College Math. J. 13(1) (1982), p. 21.
- Amin Witno, Another simple construction of Smith numbers, Missouri J. Math. Sci. 22(2) (2010), 97-101.
- Amin Witno, Smith multiples of a class of primes with small digital sum, Thai Journal of Mathematics 14(2) (2016), 491-495.
Programs
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Maple
for s from 2 to 10000 do g:=nops(ifactors(s)[2]): qsp:=0: for u from 1 to g do z:=ifactors(s)[2,u][1]: h:=0: while (z>0) do z:=iquo(z,10,'r'): h:=h+r^2: end do: h:=h*ifactors(s)[2,u][2]: qsp:=qsp+h: end do: z:=s: qs:=0: while (z>0) do z:=iquo(z,10,'r'): qs:=qs+r^2: end do: if (qsp=qs) then print(s): end if: end do:
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Mathematica
With[{k = 2},Select[Range[12000], Function[n, And[Total@ Map[#^k &, IntegerDigits@ n] == Total@ Map[#^k &, Flatten@ IntegerDigits[#]], Not[Sort@ DeleteCases[#, 0] &@ IntegerDigits@ n == Sort@ DeleteCases[#, 0] &@ #]] &@ Flatten@ Map[IntegerDigits@ ConstantArray[#1, #2] & @@ # &, FactorInteger@ n]]]] (* Michael De Vlieger, Dec 10 2016 *)
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