A102294 Number of prime divisors (with multiplicity) of icosahedral numbers.
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, 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, 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
Offset: 1
Examples
IcosahedralNumber(13) = 5083 = 13 * 17 * 23 so Omega(IcosahedralNumber(13)) = 3. IcosahedralNumber(37) = 123247 = 37 * 3331 so Omega(IcosahedralNumber(37)) = 2, hence the 37th icosahedral number is the smallest to be semiprime.
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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Mathematica
Table[PrimeOmega[n*(5*n^2-5*n+2)/2],{n,120}] (* Harvey P. Dale, Jun 06 2015 *)
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PARI
a(n)=bigomega(n)+bigomega(5*binomial(n,2)+1) \\ Charles R Greathouse IV, Mar 09 2012
Comments