A069780 a(n) = gcd(d(n^3), d(n)).

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, 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, 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

Offset

1,2

Comments

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.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A000005, A037992, A069781, A069782.

Sequence in context: A278763 A278762 A055076 * A369307 A366308 A347089

Adjacent sequences: A069777 A069778 A069779 * A069781 A069782 A069783

Keyword

nonn

Author

Labos Elemer, Apr 08 2002

Status

approved