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 A069781 Numbers k such that gcd(d(k^3), d(k)) is not a power of 2. 5
 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 (list; graph; refs; listen; history; text; internal format)
 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<; [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 * A231231 A179666 A203663 Adjacent sequences:  A069778 A069779 A069780 * A069782 A069783 A069784 KEYWORD nonn AUTHOR Labos Elemer, Apr 08 2002 STATUS approved

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Last modified May 30 11:52 EDT 2020. Contains 334724 sequences. (Running on oeis4.)