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A362139
a(n) is the smallest number k with exactly n of its divisors in A037197.
0
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
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
KEYWORD
nonn
AUTHOR
Marius A. Burtea, May 03 2023
STATUS
approved