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 A069781 Numbers n such that GCD[d(n^3), d(n)] is not a power of 2. 4
 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 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<

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Last modified February 19 07:51 EST 2019. Contains 320309 sequences. (Running on oeis4.)