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 A069782 Numbers k such that gcd(d(k^3), d(k)) = 2^w for some w. 5
 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 Andrew Howroyd, Table of n, a(n) for n = 1..10000 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: A296903 A296906 A104661 * A088480 A289207 A061019 Adjacent sequences:  A069779 A069780 A069781 * A069783 A069784 A069785 KEYWORD nonn AUTHOR Labos Elemer, Apr 08 2002 STATUS approved

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Last modified August 20 07:48 EDT 2019. Contains 326143 sequences. (Running on oeis4.)