A178203 - OEIS

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 #20 Oct 22 2019 04:21:54

%S 414966,443166,454266,1274664,1371372,1701856,1713732,1734616,1771248,

%T 1858436,1858616,2075664,2624976,3606691,3771031,3771301,4266914,

%U 4414866,4461786,4605146,4670576,4710739,5209663,5281767,5434572,5836565,5861712,5871968,6046357

%N 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 Donovan Johnson, <a href="/A178203/b178203.txt">Table of n, a(n) for n = 1..1000</a>

%H Patrick Costello, <a href="https://www.fq.math.ca/Scanned/40-4/costello.pdf">A new largest Smith number</a>, Fibonacci Quarterly 40(4) (2002), 369-371.

%H Underwood Dudley, <a href="https://www.jstor.org/stable/2690561">Smith numbers</a>, Mathematics Magazine 67(1) (1994), 62-65.

%H 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 S. S. Gupta, <a href="http://www.shyamsundergupta.com/smith.htm">Smith Numbers</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SmithNumber.html">Smith number</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Smith_number">Smith number</a>.

%H A. Wilansky, <a href="https://www.jstor.org/stable/3026531">Smith Numbers</a>, Two-Year College Math. J. 13(1) (1982), p. 21.

%H 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 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 a(10) = 1858436 = 2*2*29*37*433;

%e 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 Cf. A006753 (Smith numbers), A176670, A174460, A178213, A178193, A178204.

%K nonn,base

%O 1,1

%A _Paul Weisenhorn_, Dec 19 2010

%E a(21) corrected by _Donovan Johnson_, Jan 02 2013