A093617 -id:A093617 - cp's OEIS frontend

A093616 a(n) is the smallest k such that k*n has exactly as many divisors as n^2.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 8, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 8, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72

Offset: 1

Reinhard Zumkeller, Apr 06 2004

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000005, A000290, A048691, A093617, A093618.

a[n_] := For[k = 1, True, k++, If[DivisorSigma[0, k*n] == DivisorSigma[0, n^2], Return[k]]]; Array[a, 72] (* Jean-François Alcover, Aug 14 2014 *)

a(n) = {my(k = 1, d = numdiv(n^2)); while(numdiv(k*n) != d, k++); k;} \\ Amiram Eldar, Apr 15 2024

A000005(a(n)*n) = A000005(n^2) and A000005(m*n) <> A000005(n^2) for m < a(n).

a(A093617(n)) < n, a(A093618(n)) = n.

A093618 Numbers m such that for all k less than m the number of divisors of k*m and m^2 are different.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74

Offset: 1

Reinhard Zumkeller, Apr 06 2004

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1800 from Vincenzo Librandi)

Complement of A093617.

Cf. A000005, A000290, A048691, A093616.

A093616[n_] := For[k = 1, True, k++, If[DivisorSigma[0, k*n] == DivisorSigma[0, n^2], Return[k]]]; Select[Range[100], A093616[#] == # &] (* Jean-François Alcover, Aug 14 2014 *)

is(n) = {my(k = 1, d = numdiv(n^2)); while(k < n && numdiv(k*n) != d, k++); k == n;} \\ Amiram Eldar, Apr 15 2024

A093616(a(n)) = n.

Corrected by Franklin T. Adams-Watters, Dec 19 2006

cp's OEIS Frontend

A093616 a(n) is the smallest k such that k*n has exactly as many divisors as n^2.

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