

A102294


Number of prime divisors (with multiplicity) of icosahedral numbers.


1



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
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OFFSET

1,2


COMMENTS

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, ...


LINKS



FORMULA



EXAMPLE

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.


MATHEMATICA

Table[PrimeOmega[n*(5*n^25*n+2)/2], {n, 120}] (* Harvey P. Dale, Jun 06 2015 *)


PROG



CROSSREFS



KEYWORD

easy,nonn


AUTHOR



STATUS

approved



