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A355078 a(n) is the smallest number k with exactly n divisors in A033075.

%I A355078 #9 Sep 12 2022 03:55:27
%S A355078 1,2,4,6,18,12,24,60,120,168,360,1080,840,3360,2520,7560,15120,30240,
%T A355078 84840,196560,339360,254520,1102920,763560,1527120,4581360,3054240,
%U A355078 9162720,9926280,19852560,59557680,39705120,119115360,277935840,674987040,1151448480,1469089440
%N A355078 a(n) is the smallest number k with exactly n divisors in A033075.
%e A355078 1 has a single divisor in A033075, so a(1) = 1.
%e A355078 2 has divisors 1 and 2 in A033075, so a(2) = 2;
%e A355078 3 has only divisors 1, 3 in A033075, 4 has divisors 1, 2, 4 in A033075, so a(3) = 4.
%e A355078 5 has only divisors 1, 5 in A033075, 6 has divisors 1, 2, 3, 6 in A033075, so a(4) = 6.
%o A355078 (Magma) alt:=func<n| forall{i:i in [1..#Intseq(n)-1]|Abs(Intseq(n)[i+1]-Intseq(n)[i]) eq 1}>; a:=[]; for n in [1..37] do k:=1; while #[d:d in Divisors(k)|alt(d)] ne n do k:=k+1; end while; Append(~a,k); end for; a;
%o A355078 (PARI) diff(v)=vector(#v-1, i, v[i+1]-v[i]);
%o A355078 is(n)=if(n>9, Set(abs(diff(digits(n))))==[1], n>0);
%o A355078 a(n) = my(k=1); while (sumdiv(k, d, is(d)) != n, k++); k; \\ _Michel Marcus_, Jul 11 2022
%Y A355078 Cf. A033075.
%K A355078 nonn,base
%O A355078 1,2
%A A355078 _Marius A. Burtea_, Jul 11 2022