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A334828 Numbers that divide the multiplication of its digits raised to their own powers.

%I A334828 #20 Mar 31 2024 17:12:01
%S A334828 1,2,3,4,5,6,7,8,9,16,25,36,64,96,125,128,135,162,175,216,250,256,375,
%T A334828 378,384,432,486,567,576,625,648,672,675,729,735,756,768,784,864,875,
%U A334828 972,1024,1176,1250,1296,1372,1715,1764,1944,2048,2304,2500,2744,2916,3087,3125,3375,3456,3645,3675,4096
%N A334828 Numbers that divide the multiplication of its digits raised to their own powers.
%C A334828 As in A045503 we take 0^0 = 1.
%C A334828 Numbers m that divide A061510(m).
%H A334828 Giovanni Resta, <a href="/A334828/b334828.txt">Table of n, a(n) for n = 1..10000</a>
%e A334828 5 is a term as 5^5 = 3125 which is divisible by 5.
%e A334828 16 is a term as 1^1*6^6 = 46656 which is divisible by 16.
%e A334828 375 is a term as 3^3*7^7*5^5 = 69486440625 which is divisible by 375.
%e A334828 1176 is a term as 1^1*1^1*7^7*6^6 = 38423222208 which is divisible by 1176.
%t A334828 pow[n_] := If[n == 0, 1, n^n]; Select[Range[2^12], Divisible[Times @@ (pow /@ IntegerDigits[#]), #] &] (* _Amiram Eldar_, May 13 2020 *)
%o A334828 (PARI) isok(m) = my(d=digits(m)); (prod(k=1, #d, d[k]^d[k]) % m) == 0; \\ _Michel Marcus_, May 14 2020
%Y A334828 Cf. A000312, A045503, A046253, A061510, A243507, A108302.
%K A334828 nonn,base
%O A334828 1,2
%A A334828 _Scott R. Shannon_, May 13 2020