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A063383 a(1) = 6, a(n) = concatenation of two closest divisors of a(n-1) whose product equals a(n-1) or if a(n-1) is a prime then the concatenation of 1 and a(n-1).

%I A063383 #10 Jun 23 2021 09:58:59
%S A063383 6,23,123,341,1131,2939,12939,57227,89643,329881,1073083,1197553,
%T A063383 7171079,17171079,57301247,208327509,1171780577,1219684137,1478297171,
%U A063383 2587571433,2795835979,8663322733,13666409441,113666409441,1030771102733,2114885171103,6993025586797
%N A063383 a(1) = 6, a(n) = concatenation of two closest divisors of a(n-1) whose product equals a(n-1) or if a(n-1) is a prime then the concatenation of 1 and a(n-1).
%H A063383 Harvey P. Dale, <a href="/A063383/b063383.txt">Table of n, a(n) for n = 1..100</a>
%t A063383 f[ n_Integer ] := (d = Divisors[ n ]; l = Length[ d ]; If[ EvenQ[ l ], ToExpression[ ToString[ d[[ l/2 ] ] ] <> ToString[ d[[ l/2 + 1 ] ] ] ], ToExpression[ ToString[ d[[ l/2 + .5 ] ] ] <> ToString[ d[[ l/2 + .5 ] ] ] ] ] ); NestList[ f, 6, 25 ]
%t A063383 tcf[n_]:=Module[{d=Divisors[n],len},len=Length[d]/2;FromDigits[Flatten[ IntegerDigits/@Take[d,{len,len+1}]]]]; ctc[n_]:=If[PrimeQ[ n], 10^IntegerLength[ n]+n,tcf[n]]; NestList[ctc,6,30] (* _Harvey P. Dale_, May 19 2019 *)
%o A063383 (Python)
%o A063383 from sympy import divisors, isprime
%o A063383 def aupton(terms):
%o A063383     alst = [6]
%o A063383     for n in range(2, terms+1):
%o A063383         if isprime(alst[-1]): alst.append(int('1' + str(alst[-1])))
%o A063383         else:
%o A063383             divs = divisors(alst[-1])
%o A063383             d1 = divs[(len(divs)-1)//2]
%o A063383             d2 = alst[-1]//d1
%o A063383             alst.append(int(str(d1) + str(d2)))
%o A063383     return alst
%o A063383 print(aupton(27)) # _Michael S. Branicky_, Jun 23 2021
%Y A063383 Cf. A003681, A062094 and A062095.
%K A063383 base,nonn
%O A063383 1,1
%A A063383 _Robert G. Wilson v_, Aug 08 2001
%E A063383 Definition clarified by _Harvey P. Dale_, May 19 2019