

A104011


Number of prime factors (with multiplicity) of centered dodecahedral numbers (A005904).


1



0, 2, 2, 2, 3, 2, 2, 3, 3, 3, 4, 2, 4, 4, 2, 2, 3, 3, 3, 3, 3, 2, 4, 3, 3, 3, 2, 4, 4, 3, 2, 6, 3, 3, 4, 2, 2, 5, 3, 3, 6, 3, 4, 3, 2, 4, 4, 4, 3, 4, 3, 3, 4, 3, 2, 3, 3, 4, 5, 4, 3, 3, 4, 2, 5, 3, 3, 7, 3, 2, 3, 3, 4, 4, 2, 3, 5, 4, 3, 3, 3, 2, 4, 3, 4, 4, 4, 4, 3, 4, 3, 4, 4, 3, 5, 3, 3, 6, 3, 3
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OFFSET

0,2


COMMENTS

When a(n) = 2, n is an element of A104012: indices of centered dodecahedral numbers (A005904) which are semiprimes.


REFERENCES

B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 45454558.


LINKS

Table of n, a(n) for n=0..99.


FORMULA

a(n) = A001222(A005904(n)). a(n) = Bigomega((2*n+1)*(5*n^2 + 5*n + 1)).


EXAMPLE

a(9) = 3 because A005904(9) = 8569 = 11 * 19 * 41, which has 3 prime factors (which happen to have the same number of digits).
a(18) = 3 because A005904(18) = 63307 = 29 * 37 * 59.
a(96) = 3 because A005904(96) = 8986273 = 101 * 193 * 461.
a(126) = 5 because A005904(126) = 20242783 = 11 * 23 * 29 * 31 * 89, which has 5 prime factors (which happen to have the same number of digits).


MATHEMATICA

PrimeOmega[(2*n+1)*(5*n^2+5*n+1)] /. n > Range[0, 99] (* Giovanni Resta, Jun 17 2016 *)


CROSSREFS

Cf. A001222, A005904, A104012.
Sequence in context: A116504 A186233 A226056 * A242879 A176775 A175778
Adjacent sequences: A104008 A104009 A104010 * A104012 A104013 A104014


KEYWORD

easy,nonn


AUTHOR

Jonathan Vos Post, Feb 24 2005


EXTENSIONS

A missing term inserted by Giovanni Resta, Jun 17 2016


STATUS

approved



