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Smallest Smith number with n prime factors.
1

%I #32 Jan 05 2025 19:51:38

%S 4,27,636,378,729,648,576,2688,17496,44928,75776,168960,765952,319488,

%T 958464,5537792,5963776,2883584,5767168,7077888,279969792,544997376,

%U 778567680,2579496960,4567597056,3875536896,22749904896,60699967488,87509958656,164886478848,758296608768,199715979264,599147937792,5295694675968,446676598784,2954937499648

%N Smallest Smith number with n prime factors.

%C a(38) > 1.286e13. - _Max Alekseyev_, Oct 03 2024

%H 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 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="https://web.archive.org/web/20101017153448/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="https://thaijmath2.in.cmu.ac.th/index.php/thaijmath/article/view/612">Smith multiples of a class of primes with small digital sum</a>, Thai Journal of Mathematics 14(2) (2016), 491-495.

%e a(4) = 636 because 636 is the smallest Smith number with 4 prime factors.

%Y Cf. A006753, A104169.

%K nonn,base

%O 2,1

%A _Shyam Sunder Gupta_, Mar 10 2005 and May 03 2005

%E a(28)-a(31) from _Donovan Johnson_, Jan 02 2013

%E a(32)-a(37) from _Max Alekseyev_, Oct 01 2024