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A069781
Numbers k such that gcd(d(k^3), d(k)) is not a power of 2.
6
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
KEYWORD
nonn
AUTHOR
Labos Elemer, Apr 08 2002
STATUS
approved