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A337183 If n is composite, a(n) is the number represented by the list of prime factors of n (with multiplicity, sorted in nondecreasing order) in base the sum of that list. If n is prime, a(n) = n.

%I A337183 #19 Jan 30 2021 02:17:34
%S A337183 2,3,10,5,13,7,86,21,19,11,115,13,25,29,1170,17,155,19,185,37,37,23,
%T A337183 1641,55,43,273,271,29,235,31,22222,53,55,67,2233,37,61,61,2931,41,
%U A337183 331,43,491,401,73,47,32211,105,353,77,625,53,3061,91,4765,85,91,59,3785,61,97,553,542906,103,571,67
%N A337183 If n is composite, a(n) is the number represented by the list of prime factors of n (with multiplicity, sorted in nondecreasing order) in base the sum of that list.  If n is prime, a(n) = n.
%C A337183 If p is prime, a(p^k) = p*((k*p)^k-1)/(k*p-1).
%C A337183 If n = p*q with primes p <= q, a(n) = p^2 + p*q + q.
%H A337183 Robert Israel, <a href="/A337183/b337183.txt">Table of n, a(n) for n = 2..10000</a>
%e A337183 For n = 12, the list of prime factors is [2,2,3], the base is 2+2+3=7, and a(12) = 223_7 = 115.
%p A337183 f:= proc(n) local F,b,i;
%p A337183   F:= sort(map(t -> t[1]$t[2],ifactors(n)[2]),`>`);
%p A337183   b:= convert(F,`+`);
%p A337183   (add(F[i]*b^(i-1),i=1..nops(F)));
%p A337183 end proc:
%p A337183 map(f, [$2..100]);
%t A337183 Array[If[PrimeQ@ #, #, FromDigits[#, Total[#]] &@ Flatten[ConstantArray @@@ FactorInteger[#]]] &, 66, 2] (* _Michael De Vlieger_, Jan 29 2021 *)
%K A337183 nonn,base,look
%O A337183 2,1
%A A337183 _J. M. Bergot_ and _Robert Israel_, Jan 29 2021