This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A174460 #55 Feb 16 2025 08:33:12
%S A174460 56,58,810,822,1075,1519,1752,2145,2227,2260,2483,2618,2620,3078,3576,
%T A174460 3653,3962,4336,4823,4974,5216,5242,5386,5636,5719,5762,5935,5998,
%U A174460 6220,6424,6622,6845,7015,7251,7339,7705,7756,8460,9254,9303,9355,10481,10626,10659
%N A174460 Smith numbers of order 2.
%C A174460 Composite numbers a(n) such that the sum of digits^2 equals the sum of digits^2 of its prime factors without the numbers of A176670 that have the same digits as its prime factors (without the zero digit).
%C A174460 It seems as though as the order n approaches infinity, the sequence of n-order Smith numbers approaches A176670. Is there a value of n where the only n-order Smith numbers are members of A176670? - _Ely Golden_, Dec 07 2016
%H A174460 Ely Golden and Donovan Johnson, <a href="/A174460/b174460.txt">Table of n, a(n) for n = 1..10000</a> (terms 1 to 1000 by Donovan Johnson)
%H A174460 Patrick Costello, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/40-4/costello.pdf">A new largest Smith number</a>, Fibonacci Quarterly 40(4) (2002), 369-371.
%H A174460 Underwood Dudley, <a href="https://www.jstor.org/stable/2690561">Smith numbers</a>, Mathematics Magazine 67(1) (1994), 62-65.
%H A174460 Ely Golden, <a href="/A174460/a174460_1.sagews.txt">Smith number sequence generator optimized for order 2</a>.
%H A174460 S. S. Gupta, <a href="http://www.appliedprobability.org/data/files/MS%20issues/Vol37_No1.pdf">Smith Numbers</a>, Mathematical Spectrum 37(1) (2004/5), 27-29.
%H A174460 S. S. Gupta, <a href="http://www.shyamsundergupta.com/smith.htm">Smith Numbers</a>.
%H A174460 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SmithNumber.html">Smith number</a>.
%H A174460 Wikipedia, <a href="https://en.wikipedia.org/wiki/Smith_number">Smith number</a>.
%H A174460 A. Wilansky, <a href="https://www.jstor.org/stable/3026531">Smith Numbers</a>, Two-Year College Math. J. 13(1) (1982), p. 21.
%H A174460 Amin Witno, <a href="https://projecteuclid.org/euclid.mjms/1312233139">Another simple construction of Smith numbers</a>, Missouri J. Math. Sci. 22(2) (2010), 97-101.
%H A174460 Amin Witno, <a href="http://thaijmath.in.cmu.ac.th/index.php/thaijmath/article/view/952">Smith multiples of a class of primes with small digital sum</a>, Thai Journal of Mathematics 14(2) (2016), 491-495.
%e A174460 a(2) = 58 = 2*29 is a Smith number of order 2 because 5^2 + 8^2 = 2^2 + 2^2 + 9^2 = 89.
%p A174460 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:
%t A174460 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 *)
%Y A174460 Cf. A006753 (Smith numbers), A176670, A178213, A178193, A178203, A178204.
%K A174460 nonn,base
%O A174460 1,1
%A A174460 _Paul Weisenhorn_, Dec 20 2010