OFFSET
1,1
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..763
EXAMPLE
For n = 1 and k = 12 the set M = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11} and we obtain only 12 * 3 = 36 = 6^2, so a(1) = 12.
For n = 2 and k = 4 the set M = {1, 2, 3} and we obtain 4 * 1 = 4 = 2^2 and 4 * 2 = 8 = 2^3 so a(2) = 4.
For n = 3 and k = 8 the set M = {1, 2, 3, 4, 5, 6, 7}. The powers 8 * 1 = 2^3, 8 * 2 = 16 = 2^4 and 8 * 4 = 32 = 2^5 are obtained, so a(3) = 8.
MATHEMATICA
ppQ[n_] := 1 < GCD @@ FactorInteger[n][[All, 2]]; cnt[k_] := cnt[k] = Length[ Select[ Range[k-1], ppQ[k #] &]]; a[n_] := Block[{k = n + 1}, While[ cnt[k] != n, k++]; k]; Array[a, 40] (* Giovanni Resta, Dec 05 2019 *)
PROG
(Magma) a:=[]; for n in [1..40] do k:=1; while #[m:m in [1..k-1]| IsPower(m*k)] ne n do k:=k+1; end while; Append(~a, k); end for; a;
(PARI) a(n) = {my(k=2); while (sum(m=1, k-1, ispower(m*k) != 0) != n, k++); k; } \\ Michel Marcus, Dec 05 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Marius A. Burtea, Nov 29 2019
STATUS
approved