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

0,2

Links

Table of n, a(n) for n=0..36.

Example

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.

Prog

(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;
(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

Crossrefs

Cf. A000005, A052486.

Sequence in context: A235179 A204492 A204485 * A344179 A050498 A077535

Adjacent sequences: A358511 A358512 A358513 * A358515 A358516 A358517

Keyword

nonn

Author

Marius A. Burtea, Dec 04 2022

Status

approved