A069780 - OEIS

%I #14 Mar 25 2020 06:52:02

%S 1,2,2,1,2,4,2,2,1,4,2,2,2,4,4,1,2,2,2,2,4,4,2,8,1,4,2,2,2,8,2,2,4,4,

%T 4,1,2,4,4,8,2,8,2,2,2,4,2,2,1,2,4,2,2,8,4,8,4,4,2,4,2,4,2,1,4,8,2,2,

%U 4,8,2,2,2,4,2,2,4,8,2,2,1,4,2,4,4,4,4,8,2,4,4,2,4,4,4,4,2,2,2,1,2,8,2,8,8

%N a(n) = gcd(d(n^3), d(n)).

%C Terms are usually powers of 2. Smallest number m such that A069780(m)=2^n is A037992(n). The first n such that a(n) is not a power of 2 equals 432: a(432) = gcd(d(80621568), d(432)) = gcd(130,20) = 10.

%H Charles R Greathouse IV, <a href="/A069780/b069780.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = gcd(A000005(n^3), A000005(n)).

%t Table[GCD[DivisorSigma[0, n^3], DivisorSigma[0, n]], {n, 1, 500}]

%o (PARI) a(n)=my(f=factor(n)[, 2]); gcd(prod(i=1, #f, 3*f[i]+1), prod(i=1, #f, f[i]+1)) \\ _Charles R Greathouse IV_, Oct 16 2015

%Y Cf. A000005, A037992, A069781, A069782.

%K nonn

%O 1,2

%A _Labos Elemer_, Apr 08 2002