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 A286527 a(n) is the smallest k>1 such that d(n,k)^2 = d(n^2,k^2), where d(n,k) is the n-th divisor of a number k, for n>1; and a(1) = 1. 0
 1, 6, 70, 210, 2622, 9282, 277134, 1159710, 8064030, 56185590, 186605430, 2748628830, 5053814978, 72641163166 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Or a(n) is the smallest number k such that, if d is the n-th divisor of k, then d^2 is the (n^2)-th divisor of k^2. For n <= 14, a(n) is squarefree, and omega(a(n)) < 9. Is a(n) squarefree for all n? - David A. Corneth, May 12 2017 LINKS EXAMPLE a(2) = 6 because the divisors of 6 and 36 are {1, 2, 3, 6} and {1, 2, 3, 4, 6, 9, 12, 18, 36} respectively, and the 2nd divisor of 6 is 2, and the 4th divisor of 36 is 2^2. Hence, d(2,6)^2 = d(4,36) = 4. MATHEMATICA Do[k=1; While[!(Length[Divisors[k]]>=n&&Length[Divisors[k^2]]>=n^2&&Part[Divisors[k], n]^2==Part[Divisors[k^2], n^2]), k++]; Print[n, " ", k], {n, 1, 10}] PROG (PARI) a(n) = {if (n==1, return (1)); my(k=2); while (iferr(divisors(k)[n]^2 != divisors(k^2)[n^2], E, 1), k++); k; } \\ Michel Marcus, Sep 12 2017 CROSSREFS Cf. A027750. Sequence in context: A218683 A188406 A048708 * A104900 A186667 A001448 Adjacent sequences:  A286524 A286525 A286526 * A286528 A286529 A286530 KEYWORD nonn,more AUTHOR Michel Lagneau, May 11 2017 EXTENSIONS a(10)-a(12) from Giovanni Resta, May 12 2017 a(13)-a(14) from Giovanni Resta, May 16 2017 Name edited by Michel Marcus, Sep 15 2017 STATUS approved

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Last modified September 23 05:12 EDT 2021. Contains 347609 sequences. (Running on oeis4.)