A069782 - OEIS

%I #20 Jul 27 2018 16:55:34

%S 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,

%T 27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,

%U 50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69

%N Numbers k such that gcd(d(k^3), d(k)) = 2^w for some w.

%C The first missing integer is 432 (see in A069781).

%H Andrew Howroyd, <a href="/A069782/b069782.txt">Table of n, a(n) for n = 1..10000</a>

%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/NonRecursions.html">Non Recursions</a>

%e Below 100000 only 314 integers are missing, collected in A069781.

%t 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}]

%o (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

%Y Cf. A000005, A069780, A069781, A037992, A061701.

%K nonn

%O 1,2

%A _Labos Elemer_, Apr 08 2002