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A358514 a(n) is the smallest number with exactly n divisors that are Achilles numbers (A052486).

%I A358514 #10 Dec 25 2022 15:06:30
%S A358514 1,72,216,432,1296,864,7200,2592,6912,10800,7776,15552,27000,41472,
%T A358514 21600,31104,884736,54000,64800,129600,86400,248832,172800,162000,
%U A358514 5308416,108000,194400,216000,518400,388800,810000,1323000,1058400,1382400,324000,432000,2073600
%N A358514 a(n) is the smallest number with exactly n divisors that are Achilles numbers (A052486).
%e A358514 1 has no Achilles number divisors, so a(0) = 1.
%e A358514 72 = A052486(1), so a(1) = 72.
%e A358514 216 has divisors 72 = A052486(1) and 108 = A052486(2), and there are no smaller numbers that have exactly two divisors that are Achilles numbers, so a(2) = 216.
%o A358514 (Magma) ah:=func<n|n ne 1 and forall{i:i in [1..#Factorisation(n)] |Factorisation(n)[i][2] gt 1} and Gcd([Factorisation(n)[i][2] :i in [1..#Factorisation(n)]]) eq 1>; a:=[]; for n in [0..37] do k:=1; while #[d:d in Divisors(k)| ah(d)] ne n do k:=k+1; end while; Append(~a,k); end for; a;
%o A358514 (PARI) is(n) = my(f=factor(n)[, 2]); n>9 && vecmin(f)>1 && gcd(f)==1; \\ A052486
%o A358514 a(n) = my(k=1); while (sumdiv(k, d, is(d)) != n, k++); k; \\ _Michel Marcus_, Dec 13 2022
%Y A358514 Cf. A000005, A052486.
%K A358514 nonn
%O A358514 0,2
%A A358514 _Marius A. Burtea_, Dec 04 2022