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Search: id:A104414
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| A104414 |
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Number of prime factors, with multiplicity, of the heptanacci numbers A066178. |
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+0
6
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| 0, 0, 1, 2, 3, 4, 5, 6, 1, 2, 6, 3, 7, 6, 9, 8, 1, 4, 2, 5, 6, 5, 8, 9, 2, 3, 10, 6, 7, 7, 16
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Prime heptanacci numbers: a(2) = 2, a(8) = 127, a(16) = 31489, ... Semiprime heptanacci numbers: a(4) = 4 = 2^2, a(9) = 253 = 11 * 23, a(18) = 124946 = 2 * 62473, a(24) = 7805695 = 5 * 1561139.
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FORMULA
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a(n) = A001222(A066178(n)). a(n) = bigomega(A066178(n)).
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EXAMPLE
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a(0)=a(1)=0 because the first two nonzero heptanacci numbers are both 1, which has zero prime divisors.
a(2)=1 because the 3rd nonzero heptanacci number is 2, a prime, with only one prime divisor.
a(3)=2 because the 4th nonzero pentanacci number is 4 = 2^2 which has (with multiplicity) 2 prime divisors (which happen to be equal).
a(4)=3 because the 5th nonzero heptanacci number is 8 = 2^3.
a(12)= 7 because A066178(12) = 2000 = 2^4 * 5^3 which has seven prime factors (four of the 2, three of them 5).
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CROSSREFS
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Cf. A001222, A066178, A104411, A104412, A104413.
Sequence in context: A010885 A053828 A033927 this_sequence A125934 A125935 A138776
Adjacent sequences: A104411 A104412 A104413 this_sequence A104415 A104416 A104417
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 06 2005
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