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

1, 72, 216, 432, 1296, 864, 7200, 2592, 6912, 10800, 7776, 15552, 27000, 41472, 21600, 31104, 884736, 54000, 64800, 129600, 86400, 248832, 172800, 162000, 5308416, 108000, 194400, 216000, 518400, 388800, 810000, 1323000, 1058400, 1382400, 324000, 432000, 2073600

Offset: 0

Author

Marius A. Burtea, Dec 04 2022

Keywords

• nonn

Examples

			1 has no Achilles number divisors, so a(0) = 1.
72 = A052486(1), so a(1) = 72.
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.
		

Crossrefs

Cf. A000005, A052486.

Programs

Magma

ah:=func; 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;

PARI

is(n) = my(f=factor(n)[, 2]); n>9 && vecmin(f)>1 && gcd(f)==1; \\ A052486
a(n) = my(k=1); while (sumdiv(k, d, is(d)) != n, k++); k; \\ Michel Marcus, Dec 13 2022