Search: id:A106482
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%I A106482
%S A106482 0,0,2,2,3,3,3,2,4,4,3,2,5,2,4,3,6,2,4,3,5,3,3,3,5,3,4,5,4,3,5,3,7,4,3,
%T A106482 4,5,4,3,3,6,2,4,2,6,4,3,3,7,3,4,4,4,3,8,4,5,4,5,2,6,3,3,4,7,5,5,3,5,3,
%U A106482 5,3,7,2,4,5,4,4,5,3,6,5,5,3,6,3,4,3,6,4,6,3,4,5,4,3,8,3,4,5,6
%N A106482 Number of prime factors (with multiplicity) of the Stella Octangula numbers 
               A007588.
%C A106482 Because of the polynomial factorization, the Stella Octangula numbers 
               can never be prime. They are semiprime when n = is prime and 2*n^2-1 
               is also prime. That is, the n-th Stella Octangula number is semiprime 
               for n = 2, 3, 7, 11, 13, 17, 41, 43, 59, 73, 109, 113, 127, 137, 
               157, 179, 181, 197, 199, ...; that sequence is A106483.
%H A106482 J. V. Post, <a href="http://www.magicdragon.com/poly.html">Table of Polytope 
               Numbers, Sorted, Through 1,000,000</a>
%H A106482 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               StellaOctangulaNumber.html">Stella Octangula Number.</a>
%F A106482 a(n) = A001222(A007588(n)).
%e A106482 73*(2*73^2 - 1) = 777961 = 73 * 10657, which has two prime factors, so 
               a(73) = 2.
%e A106482 100*(2*100^2 - 1) = 1999900 = 2^2 * 5^2 * 7 * 2857 has 6 prime factors.
%Y A106482 Cf. A000040, A001222, A007588, A106483, A106484.
%Y A106482 Sequence in context: A108133 A014499 A055778 this_sequence A122462 A165024 
               A157639
%Y A106482 Adjacent sequences: A106479 A106480 A106481 this_sequence A106483 A106484 
               A106485
%K A106482 easy,nonn
%O A106482 0,3
%A A106482 Jonathan Vos Post (jvospost3(AT)gmail.com), May 03 2005

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