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Search: id:A104412
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| A104412 |
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Number of prime factors, with multiplicity, of the pentanacci numbers A001591. |
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+0
5
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| 0, 0, 1, 2, 3, 4, 1, 1, 5, 3, 5, 6, 2, 4, 6, 5, 9, 6, 2, 2, 6, 4, 6, 7, 1, 3, 3, 6, 4, 7, 4, 2, 7
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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I am using a(-3)=a(-2)=a(-1)=a(0)=0, a(1)=1 here. Prime pentanacci numbers: a(7) = 31, a(8) = 61, a(25) = 5976577, ... Semiprime pentanacci numbers: a(4) = 4 = 2^2, a(13) = 1793 = 11 * 163, a(19) = 103519 = 13 * 7963, a(20) = 203513 = 113 * 1801, a(32) = 678355061 = 673 * 1007957
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FORMULA
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a(n) = A001222(A001591(n)). a(n) = bigomega(A001591(n)).
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EXAMPLE
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a(1)=a(2)=0 because the first two nonzero pentanacci numbers are both 1, which has zero prime divisors.
a(3)=1 because the 3rd nonzero pentanacci number is 2, a prime, with only one prime divisor.
a(4)=2 because the 4th nonzero pentanacci number is 4 = 2^2 which has (with multiplicity) 2 prime divisors (which happen to be equal).
a(5)=3 because the 5th nonzero pentanacci number is 8 = 2^3.
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CROSSREFS
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Cf. A001591, A001222, A104411.
Sequence in context: A086196 A138297 A139458 this_sequence A118310 A073057 A084310
Adjacent sequences: A104409 A104410 A104411 this_sequence A104413 A104414 A104415
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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 05 2005
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