id:A102294 - OEIS Search Results

Search: id:A102294

Displaying 1-1 of 1 results found.

page 1

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

+0
2

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, 6, 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, 5, 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 (list; graph; listen)

	OFFSET	`1,2`
	COMMENT	`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(5n^2 - 5*n + 2)/2 is prime, as with n = 31, 61, ...`
	FORMULA	`a(n) = A001222(A006564(n)). Bigomega(n(5n^2 - 5*n + 2)/2).`
	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.`
	CROSSREFS	`Cf. A001222, A006564.` `Sequence in context: A092553 A112755 A126659 this_sequence A021287 A124887 A097524` `Adjacent sequences: A102291 A102292 A102293 this_sequence A102295 A102296 A102297`
	KEYWORD	`easy,nonn`
	AUTHOR	`Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 19 2005`

page 1

Search completed in 0.002 seconds

Last modified November 30 22:12 EST 2008. Contains 150989 sequences.

AT&T Labs Research