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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 (list; graph; refs; listen; history; text; internal format)
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), 4545-4558.

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

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Last modified November 18 04:44 EST 2019. Contains 329248 sequences. (Running on oeis4.)