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

Author

Labos Elemer, Apr 08 2002

Keywords

• nonn

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

Examples

			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.
		

Links

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

Crossrefs

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

Programs

Magma

f:=func; [k:k in [1..14000]| not IsIntegral(Log(2,f(k)))]; // Marius A. Burtea, Oct 18 2019

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 *)

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<Charles R Greathouse IV, Oct 16 2015

Formula

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