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A338166 Terms of A338039 that are repeated concatenations of smaller integers.

%I A338166 #21 Oct 28 2021 01:59:48
%S A338166 1818,8181,181818,198198,405405,484848,504504,565656,576576,656565,
%T A338166 675675,818181,848484,891891,11311131,13041304,13111311,18181818,
%U A338166 19981998,22622262,26222622,33933393,39333933,40314031,41544154,45144514,46364636,63646364,81818181,87498749,89918991,94789478
%N A338166 Terms of A338039 that are repeated concatenations of smaller integers.
%H A338166 Michel Marcus, <a href="/A338166/b338166.txt">Table of n, a(n) for n = 1..1050</a> (up to 15 digits).
%H A338166 Daniel Tsai, <a href="https://arxiv.org/abs/2010.03151">A recurring pattern in natural numbers of a certain property</a>, arXiv:2010.03151 [math.NT], 2020.
%H A338166 Daniel Tsai, <a href="http://math.colgate.edu/~integers/v32/v32.mail.html">A recurring pattern in natural numbers of a certain property</a>, Integers (2021) Vol. 21, Article #A32.
%t A338166 Block[{f}, f[1] = 0; f[n_] := Plus @@ #[[All, 1]] + Plus @@ Select[#[[All, -1]], # > 1 &] &@ FactorInteger[n]; Select[Union@ Flatten@ Table[Union@ Flatten@ Map[Function[k, Map[FromDigits[Join @@ ConstantArray[IntegerDigits[#], n/k]] &, Range[10^(k - 1), 10^k - 1]]], Most@ Divisors[n]], {n, 3, 8}], And[Mod[#1, 10] != 0, #2 != #1, f[#1] == f[#2]] & @@ {#, IntegerReverse[#]} &] ] (* _Michael De Vlieger_, May 27 2021, after _Amiram Eldar_ at A338039 *)
%o A338166 (PARI) f(n) = my(f=factor(n)); vecsum(f[,1]) + sum(k=1, #f~, if (f[k,2]!=1, f[k,2])); \\ A338038
%o A338166 isok(m) = my(r=fromdigits(Vecrev(digits(m)))); if ((r != m) && (f(r) == f(m)), return(m));
%o A338166 listc(c) = {my(list = List()); fordiv(c, d, if ((d != 1) && (d != c), for(k=10^(d-1), 10^d, if (k % 10, my(sk = Str(k), skk = sk); for (j=1, c/d-1, sk = concat(sk, skk)); if (isok(eval(sk)), listput(list, eval(sk))););););); list;}
%o A338166 lista(nn) = {my(list = List()); forcomposite(c=1, nn, my(clist = Vec(listc(c))); for (k=1, #clist, listput(list, clist[k]));); vecsort(Vec(list),,8);}
%o A338166 lista(8) \\ to get terms up to 8 digits
%Y A338166 Cf. A338038, A338039.
%K A338166 nonn,base
%O A338166 1,1
%A A338166 _Michel Marcus_, Oct 14 2020