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A106482 Number of prime factors (with multiplicity) of the Stella Octangula numbers A007588. 2
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, 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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.

LINKS

Table of n, a(n) for n=0..100.

J. V. Post, Table of Polytope Numbers, Sorted, Through 1,000,000

Eric Weisstein's World of Mathematics, Stella Octangula Number.

FORMULA

a(n) = A001222(A007588(n)).

EXAMPLE

73*(2*73^2 - 1) = 777961 = 73 * 10657, which has two prime factors, so a(73) = 2.

100*(2*100^2 - 1) = 1999900 = 2^2 * 5^2 * 7 * 2857 has 6 prime factors.

CROSSREFS

Cf. A000040, A001222, A007588, A106483, A106484.

Sequence in context: A175453 A014499 A055778 * A301805 A260236 A122462

Adjacent sequences:  A106479 A106480 A106481 * A106483 A106484 A106485

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, May 03 2005

STATUS

approved

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Last modified November 18 09:46 EST 2019. Contains 329261 sequences. (Running on oeis4.)