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A346563 a(n) = n + A007978(n).

%I A346563 #26 Aug 16 2021 22:11:37
%S A346563 3,5,5,7,7,10,9,11,11,13,13,17,15,17,17,19,19,22,21,23,23,25,25,29,27,
%T A346563 29,29,31,31,34,33,35,35,37,37,41,39,41,41,43,43,46,45,47,47,49,49,53,
%U A346563 51,53,53,55,55,58,57,59,59,61,61,67,63,65,65,67,67
%N A346563 a(n) = n + A007978(n).
%C A346563 Beginning at n=3, a(n) represents the maximum length of consecutive numbers that are divisible by the product of their nonzero digits in base n. In particular, if n=10, the sequence of numbers that are divisible by the product of their nonzero digits is given by A055471.
%F A346563 a(2k+1) = 2k+3.
%F A346563 a(2k) >= 2k+3.
%e A346563 For n=6, the least non-divisor of 6 is 4, so a(6) = 6+4 = 10. As seen in the Comments section, 55980, 55981, ..., 55989 form a sequence of length 10, where every number is divisible by the product of its nonzero digits in base n=6. Work has been done to show that 10 is the maximum length for such sequences.
%t A346563 a[n_] := Module[{k = 1}, While[Divisible[n, k], k++]; n + k]; Array[a, 100] (* _Amiram Eldar_, Jul 23 2021 *)
%o A346563 (Python)
%o A346563 goal = 100
%o A346563 these = []
%o A346563 n = 1
%o A346563 while n <= goal:
%o A346563     k = 1
%o A346563     while n % k == 0:
%o A346563         k = k + 1
%o A346563     these.append(n + k)
%o A346563     n += 1
%o A346563 print(these)
%o A346563 (PARI) a(n) = my(k=2); while(!(n % k), k++); n+k; \\ _Michel Marcus_, Jul 23 2021
%Y A346563 Cf. A000027, A007978, A055471.
%K A346563 nonn,easy
%O A346563 1,1
%A A346563 _Michael Gohn_, _Joshua Harrington_, _Sophia Lebiere_, _Hani Samamah_, _Kyla Shappell_, _Wing Hong Tony Wong_, Jul 23 2021