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A178203 Smith numbers of order 5; composite numbers n such that sum of digits^5 equal sum of digits^5 of its prime factors without the numbers in A176670 that have the same digits as its prime factors (without the zero digits).

%I A178203 #22 Feb 16 2025 08:33:12
%S A178203 414966,443166,454266,1274664,1371372,1701856,1713732,1734616,1771248,
%T A178203 1858436,1858616,2075664,2624976,3606691,3771031,3771301,4266914,
%U A178203 4414866,4461786,4605146,4670576,4710739,5209663,5281767,5434572,5836565,5861712,5871968,6046357
%N A178203 Smith numbers of order 5; composite numbers n such that sum of digits^5 equal sum of digits^5 of its prime factors without the numbers in A176670 that have the same digits as its prime factors (without the zero digits).
%H A178203 Donovan Johnson, <a href="/A178203/b178203.txt">Table of n, a(n) for n = 1..1000</a>
%H A178203 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 A178203 Underwood Dudley, <a href="https://www.jstor.org/stable/2690561">Smith numbers</a>, Mathematics Magazine 67(1) (1994), 62-65.
%H A178203 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 A178203 S. S. Gupta, <a href="http://www.shyamsundergupta.com/smith.htm">Smith Numbers</a>.
%H A178203 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SmithNumber.html">Smith number</a>.
%H A178203 Wikipedia, <a href="https://en.wikipedia.org/wiki/Smith_number">Smith number</a>.
%H A178203 A. Wilansky, <a href="https://www.jstor.org/stable/3026531">Smith Numbers</a>, Two-Year College Math. J. 13(1) (1982), p. 21.
%H A178203 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 A178203 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 A178203 a(10) = 1858436 = 2*2*29*37*433;
%e A178203 1^5 + 3^5 + 4^5 + 5^5 + 6^5 + 2*8^5 = 3*2^5 + 3*3^5 + 4^5 + 7^5 + 9^5 = 77705.
%Y A178203 Cf. A006753 (Smith numbers), A176670, A174460, A178213, A178193, A178204.
%K A178203 nonn,base
%O A178203 1,1
%A A178203 _Paul Weisenhorn_, Dec 19 2010
%E A178203 a(21) corrected by _Donovan Johnson_, Jan 02 2013