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A219338 Numbers n for which n = (tau(n) - 1)^k with integer k. 1
4, 16, 27, 3125, 3375, 65536, 823543, 3748096, 52521875, 285311670611, 7625597484987, 302875106592253, 1156831381426176, 66182427701415936, 827240261886336764177, 511324276025564512546607, 1978419655660313589123979, 281633339785852578930098176 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 15 18:59 EST 2019. Contains 329149 sequences. (Running on oeis4.)