%I #8 May 06 2020 01:46:43
%S 4,666,28182,45054,51315,82628,239932,454454,864468,2594952,2976792,
%T 3189813,3355533,4172714,4890984,5319135,5367635,5777775,7149417,
%U 7247427,8068608,8079708,8100018,8280828,8627268,9227229,9423249,21699612,22544522,24166142,27677672
%N Palindromic numbers that are also Niven numbers and Smith numbers.
%C Witno (2014) proved that this sequence is infinite.
%H Amiram Eldar, <a href="/A334528/b334528.txt">Table of n, a(n) for n = 1..512</a>
%H Amin Witno, <a href="https://www.emis.de/journals/INTEGERS/papers/o66/o66.Abstract.html">Smith Numbers With Extra Digital Features</a>, Integers, Vol. 14 (2014), Article A66.
%e 666 is a term since it is palindromic, a Niven number (6 + 6 + 6 = 18 is a divisor of 666) and a Smith number (666 = 2 * 3 * 3 * 37 and 6 + 6 + 6 = 2 + 3 + 3 + 3 + 7).
%t digSum[n_] := Plus @@ IntegerDigits[n]; palNivenSmithQ[n_] := PalindromeQ[n] && Divisible[n, (ds = digSum[n])] && CompositeQ[n] && Plus @@ (Last@# * digSum[First@#] & /@ FactorInteger[n]) == ds; Select[Range[10^5], palNivenSmithQ]
%Y Intersection of A002113, A005349 and A006753.
%Y Intersection of any two of the sequences A082232, A098834 and A334527.
%K nonn,base
%O 1,1
%A _Amiram Eldar_, May 05 2020