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

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

Author

Reinhard Zumkeller, Apr 06 2004

Keywords

• nonn

Links

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

Crossrefs

Complement of A093617.

Cf. A000005, A000290, A048691, A093616.

Programs

Mathematica

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 *)

PARI

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

Formula

A093616(a(n)) = n.

Extensions

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