A362139 a(n) is the smallest number k with exactly n of its divisors in A037197.

1, 2, 8, 24, 96, 312, 600, 2100, 1800, 5400, 4200, 8400, 12600, 25200, 16800, 58800, 50400, 67200, 93600, 131040, 201600, 252000, 218400, 468000, 882000, 873600, 1386000, 1528800, 2646000, 655200, 2217600, 2772000, 4233600, 2620800, 9374400, 1965600, 3276000

Offset

1,2

Links

Table of n, a(n) for n=1..37.

Example

1 has only the divisor 1 = A037197(1), so a(1) = 1.
2 has divisors 1 = A037197(1) and 2 = A037197(2), so a(2) = 2.
3, 4, 5, 6, 7 do not have three divisors in A037197 and 8 has divisors 1 = A037197(1), 2 = A037197(2), 8 = A037197(3), so a(3) = 8.

Mathematica

seq[len_, kmax_] := Module[{s = Table[0, {len}], c = 0, k = 1, ind}, While[k < kmax && c < len, ind = DivisorSum[k, 1 &, DivisorSigma[0, DivisorSigma[1, #]] == DivisorSigma[0, #] &]; If[ind <= len && s[[ind]] == 0, c++; s[[ind]] = k]; k++]; s]; seq[20, 10^6] (* Amiram Eldar, May 05 2023 *)

Prog

(Magma) f:=func<n|#Divisors(DivisorSigma(1, n)) eq #Divisors(n)>; a:=[]; for n in [1..37] do k:=1; while #[d:d in Divisors(k)|f(d)]  ne n do k:=k+1; end while; Append(~a, k); end for; a;

Crossrefs

Cf. A000005, A000203, A037197, A062068.

Sequence in context: A106189 A106183 A357160 * A060899 A213951 A150665

Adjacent sequences: A362136 A362137 A362138 * A362140 A362141 A362142

Keyword

nonn

Author

Marius A. Burtea, May 03 2023

Status

approved