A219338 Numbers n for which n = (tau(n) - 1)^k with integer k.

4, 16, 27, 3125, 3375, 65536, 823543, 3748096, 52521875, 285311670611, 7625597484987, 302875106592253, 1156831381426176, 66182427701415936, 827240261886336764177, 511324276025564512546607, 1978419655660313589123979, 281633339785852578930098176

Offset

1,1

Comments

tau(n) is the number of positive divisors of n.

Links

Table of n, a(n) for n=1..18.

Formula

Numbers n for which n = (tau(n) - 1)^k with integer k.

Example

a(1) = 4 because (tau(4) - 1)^2 = (3 - 1)^2 = 4 and this is the first number satisfying this condition.
a(2) = 16 because (tau(16) - 1)^2 = (5 - 1)^2 = 16 and this is the second number satisfying this condition.
a(3) = 27 because (tau(27) - 1)^3 = (4 - 1)^3 = 27 and this is the third number satisfying this condition.

Mathematica

Select[Range[10^4], IntegerQ[Log[DivisorSigma[0, #] - 1, #]] &] (* Alonso del Arte, Nov 18 2012 *)

Prog

(PARI) v=vector(18); mx=3*10^26; c=0; for(m=2, 3440639, for(k=2, 87, n=m^k; if(n>mx, next(2)); if(m==numdiv(n)-1, c++; v[c]=n))); v=vecsort(v); for(i=1, c, print1(v[i]", ")) /* Donovan Johnson, Nov 19 2012 */

Crossrefs

Cf. A180936.

Sequence in context: A046358 A046366 A227609 * A275211 A046361 A228167

Adjacent sequences: A219335 A219336 A219337 * A219339 A219340 A219341

Keyword

nonn

Author

Zdenek Cervenka, Nov 18 2012

Extensions

a(10)-a(18) from Donovan Johnson, Nov 19 2012

Status

approved