A069781 Numbers k such that gcd(d(k^3), d(k)) is not a power of 2.

432, 576, 648, 1600, 2000, 2160, 2880, 2916, 3024, 3136, 3240, 4032, 4536, 4752, 4800, 5000, 5488, 5616, 6000, 6336, 7128, 7344, 7488, 7744, 8208, 8424, 9408, 9792, 9936, 10125, 10800, 10816, 10944, 11016, 11200, 12312, 12528, 13248, 13392

Offset

1,1

Comments

The complement of this sequence in the positive integers A000027 is A069782. - M. F. Hasler, Jan 18 2015

The numbers of the form 4*3^(7*m - 1), m >= 1, are terms. - Marius A. Burtea, Oct 18 2019

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

log_2(gcd(A000005(n^3), A000005(n))) is nonintegral.

Example

For n<100000, gcd[d(n^3),d[n]] = {5,7,10,14,20,28,40,80} which is obtained for n={20736,576,432,2880,54000,20160,2160,15120} respectively.

Mathematica

f[x_] := GCD[DivisorSigma[0, x^3], DivisorSigma[0, x]] Do[s=f[n]; If[ !IntegerQ[Log[2, s]], Print[n]], {n, 1, 100000}]
Select[Range[14000], !IntegerQ[Log[2, GCD[DivisorSigma[0, #^3], DivisorSigma[ 0, #]]]]&] (* Harvey P. Dale, Mar 20 2018 *)

Prog

(PARI) is(n)=my(f=factor(n)[, 2], g=gcd(prod(i=1, #f, 3*f[i]+1), prod(i=1, #f, f[i]+1))); g!=1<<valuation(g, 2) \\ Charles R Greathouse IV, Oct 16 2015
(Magma) f:=func<n| Gcd(#Divisors(n^3), #Divisors(n))>; [k:k in [1..14000]| not IsIntegral(Log(2, f(k)))]; // Marius A. Burtea, Oct 18 2019

Crossrefs

Cf. A000005, A061701, A037992, A069780, A069782.

Sequence in context: A205192 A066419 A245469 * A337670 A231231 A179666

Adjacent sequences: A069778 A069779 A069780 * A069782 A069783 A069784

Keyword

nonn

Author

Labos Elemer, Apr 08 2002

Status

approved