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 A333457 #31 Sep 08 2022 08:46:25
%S A333457 18,42,84,126,252,756,1998,1596,2394,4662,4788,9324,18648,23940,46620,
%T A333457 93240,139860,177156,559440,354312,708624,1062936,885780,4606056,
%U A333457 1771560,3543120,5314680,10629360,38974320,23030280,46060560,69090840,138181680,506666160
%N A333457 a(n) is the smallest number with exactly n divisors that are Moran numbers, or -1 if no such number exists.
%C A333457 m is a Moran number if (m / sum of digits of m) is prime (A001101).
%C A333457 Conjecture: For every n there is at least one number k with n divisors Moran numbers.
%C A333457 Conjecture: The terms are divisible by 6.
%C A333457 a(1) = 18, a(2) = 42 and a(3) = 84 are Moran numbers. Not all terms in the sequence are Moran numbers. For example: a(4) = 126 has digsum(126) = 9 and 126 / 9 = 14. Also, the terms a(5) - a(34) are not Moran numbers.
%e A333457 Of the divisors of 18 (1, 2, 3, 6, 9, 18), only 18 is a Moran number: 18 / digsum (18) = 2.
%e A333457 Of the divisors of 84 (1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84), only 21, 42 and 84 are Moran numbers: 21 / digsum (21) = 7, 42 / digsum (42) = 7 and 84 / digsum (84) = 7.
%t A333457 numDiv[n_] := DivisorSum[n, 1 &, PrimeQ[#/Plus @@ IntegerDigits[#]] &]; a[n_] := Module[{k = 1}, While[numDiv[k] != n, k++]; k]; Array[a, 20] (* _Amiram Eldar_, May 11 2020 *)
%o A333457 (Magma) a:=[]; for n in [1..20] do m:=1; while #[d:d in Divisors(m)|d mod &+Intseq(d) eq 0 and IsPrime(d div &+Intseq(d))] ne n do m:=m+1; end while; Append(~a,m); end for; a;
%Y A333457 Cf. A001101, A007953 (sum of digits), A333456.
%K A333457 nonn,base
%O A333457 1,1
%A A333457 _Marius A. Burtea_, May 03 2020