OFFSET
1,1
COMMENTS
For prime p > (2n)^(1/3), p^3 does not divide binomial(2n,n).
LINKS
Chai Wah Wu, Table of n, a(n) for n = 1..100
FORMULA
a(n) = (prime(n)^3 + 1)/2 for n>1.
Product_{n>=1} (1 - 1/a(n)) = (54/49)*zeta(6)/zeta(3)^2. - Amiram Eldar, Jun 08 2022
MATHEMATICA
t3=Table[f=FactorInteger[Binomial[2n, n]]; s=Select[f, #[[2]]>2&]; If[s=={}, 0, s[[ -1, 1]]], {n, 15000}]; Table[p=Prime[i]; First[Flatten[Position[t3, p]]], {i, PrimePi[Max[t3]]}]
lst={7}; Do[AppendTo[lst, (DivisorSigma[3, Prime[n]])/2], {n, 2, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Mar 11 2009 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
T. D. Noe, Jul 22 2005
STATUS
approved