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A069780
a(n) = gcd(d(n^3), d(n)).
6
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
KEYWORD
nonn
AUTHOR
Labos Elemer, Apr 08 2002
STATUS
approved