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%I #11 Jun 06 2015 14:35:12
%S 0,3,5,3,3,5,3,5,3,4,5,4,3,7,4,5,3,5,5,5,3,6,4,5,4,5,6,5,3,11,3,7,4,5,
%T 9,6,2,6,5,6,3,5,4,6,4,6,5,6,3,6,6,5,3,7,5,7,4,4,6,6,2,8,6,8,4,6,6,5,
%U 3,6,5,6,3,5,6,4,4,7,3,8,6,6,6,5,3,6,5,5,4,8,5,5,3,8,6,8,3,7,10,6
%N Number of prime divisors (with multiplicity) of icosahedral numbers.
%C Because the cubic factors into n time a quadratic, the icosahedral numbers can never be prime, but can be semiprime (only if n is prime and also n*(5*n^2 - 5*n + 2)/2 is prime, as with n = 31, 61, ...
%F a(n) = A001222(A006564(n)). Bigomega(n*(5*n^2 - 5*n + 2)/2).
%e IcosahedralNumber(13) = 5083 = 13 * 17 * 23 so Omega(IcosahedralNumber(13)) = 3.
%e IcosahedralNumber(37) = 123247 = 37 * 3331 so Omega(IcosahedralNumber(37)) = 2, hence the 37th icosahedral number is the smallest to be semiprime.
%t Table[PrimeOmega[n*(5*n^2-5*n+2)/2],{n,120}] (* _Harvey P. Dale_, Jun 06 2015 *)
%o (PARI) a(n)=bigomega(n)+bigomega(5*binomial(n,2)+1) \\ _Charles R Greathouse IV_, Mar 09, 2012
%Y Cf. A001222, A006564.
%K easy,nonn
%O 1,2
%A _Jonathan Vos Post_, Feb 19 2005
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