cp's OEIS Frontend

A059405 Numbers that are the product of their digits raised to positive integer powers.

%I A059405 #10 Jan 10 2020 09:18:46
%S A059405 1,2,3,4,5,6,7,8,9,128,135,175,384,432,672,735,1296,1715,6144,6912,
%T A059405 13824,18432,23328,34992,82944,93312,131712,248832,442368,1492992,
%U A059405 2239488,2333772,2612736,3981312,4128768,4741632,9289728,12192768
%N A059405 Numbers that are the product of their digits raised to positive integer powers.
%C A059405 The second example suggests that a repeated digit must divide the number at least as many times as it occurs, i.e., "distinct [digits]" in the definition would give a different (super)set. What would be the additional terms? - _M. F. Hasler_, Jan 05 2020
%H A059405 Reinhard Zumkeller, <a href="/A059405/b059405.txt">Table of n, a(n) for n = 1..120</a>
%e A059405 a(17) = 1296 = (1)(2^2)(9)(6^2);
%e A059405 a(32) = 2333772 = (2)(3)(3)(3^3)(7)(7^3)(2).
%o A059405 (Haskell)
%o A059405 a059405 n = a059405_list !! (n-1)
%o A059405 a059405_list = filter f a238985_list where
%o A059405    f x = all (== 0) (map (mod x) digs) && g x digs where
%o A059405          g z []         = z == 1
%o A059405          g z ds'@(d:ds) = r == 0 && (h z' ds' || g z' ds)
%o A059405                           where (z', r) = divMod z d
%o A059405          h z []         = z == 1
%o A059405          h z ds'@(d:ds) = r == 0 && h z' ds' || g z ds
%o A059405                           where (z', r) = divMod z d
%o A059405          digs = map (read . return) $ filter (/= '1') $ show x
%o A059405 -- _Reinhard Zumkeller_, Apr 29 2015
%Y A059405 Subsequence of A238985.
%K A059405 base,nice,nonn
%O A059405 1,2
%A A059405 _Erich Friedman_, Jan 29 2001
%E A059405 More terms from _Erich Friedman_, Apr 01 2003
%E A059405 Offset changed by _Reinhard Zumkeller_, Apr 29 2015