This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A307458 #24 Apr 10 2019 04:41:44
%S A307458 6,10,18,36,54,96,100,162,200,216,256,324,486,1296,1458,2916,4374,
%T A307458 5832,13122,26244,39366,46656,47250,49000,65536,82944,104976,118098,
%U A307458 157464,181500,236196,354294,746496,1062882,1492992,1679616,1990656,2125764,3188646,3538944
%N A307458 Composites c where an integer b with 1 < b < c exists such that when the k digits in the base-b expansion of c are considered as exponents in an ordered list of primes prime(1), prime(2), ..., prime(k), then Product_{i=1..k} prime(i)^d[i] = c, where d[h] gives the h-th most significant digit in the expansion.
%C A307458 In other words, integers k where an integer b with 1 < b < k exists such that row k of A067255 gives the digits of the base-b expansion of k.
%C A307458 Clearly, all terms are even, since all expansions start with a nonzero digit and thus the factorization of each term contains the prime 2.
%e A307458 The base-4 expansion of 200 is 3020. 2^3 * 3^0 * 5^2 * 7^0 = 200, so 200 is a term of the sequence.
%t A307458 base[n_] := Block[{e, t=0, m, b=0, s=False, p, x, pp}, pp = PrimePi@ FactorInteger[n][[-1, 1]]; If[2^(pp - 1) > n, 0, e = IntegerExponent[n, Prime@ Range@ pp]; m = Max[e] + 1; p = Total[Reverse[e] x^Range[0, Length[e] - 1]]; While[((p x^t) /. x -> m ) <= n, s = Reduce[p x^t == n && m <= x < n, x, Integers]; If[s === False, t++, b = x /. List[ToRules@ s][[1]]; Break[], t++]]; b]]; Select[Range[4, 10^5, 2], base[#] > 0 &] (* _Giovanni Resta_, Apr 10 2019 *)
%o A307458 (PARI) is(n) = for(b=2, n-1, my(d=digits(n, b), k=#d, x=1); while(k > 0, x=x*prime(k)^d[k]; k--); if(x==n, return(1))); 0
%o A307458 for(t=1, oo, if(is(2*t), print1(2*t, ", ")))
%Y A307458 Cf. A067255.
%K A307458 nonn,base
%O A307458 1,1
%A A307458 _Felix Fröhlich_, Apr 09 2019
%E A307458 a(21)-a(40) from _Giovanni Resta_, Apr 10 2019