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 A069782 Numbers n such that GCD(d(n^3),d(n)) = 2^w for some w. 4
 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The first missing integer is 432 (see in A069781). LINKS Tanya Khovanova, Non Recursions EXAMPLE Below 100000 only 314 integers are missing, collected in A069781. MATHEMATICA f[x_] := GCD[DivisorSigma[0, x^3], DivisorSigma[0, x]]; Do[s=f[n]; If[IntegerQ[Log[2, s]], Print[{n, s}]], {n, 1, 100000}] 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>>valuation(g, 2)==1 \\ Charles R Greathouse IV, Oct 16 2015 CROSSREFS Cf. A000005, A069780, A069781, A037992, A061701. Sequence in context: A104661 * A088480 A289207 A061019 A028310 A097045 Adjacent sequences:  A069779 A069780 A069781 * A069783 A069784 A069785 KEYWORD nonn AUTHOR Labos Elemer, Apr 08 2002 STATUS approved

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