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Search: id:A077218
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| A077218 |
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Sum of numbers of prime factors (counted with multiplicities) of numbers between n-th and (n+1)-th prime. |
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+0
2
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| 0, 2, 2, 7, 3, 8, 3, 7, 14, 3, 15, 8, 3, 8, 15, 14, 4, 16, 8, 5, 13, 11, 14, 21, 10, 3, 9, 5, 10, 36, 12, 16, 3, 26, 4, 16, 17, 8, 16, 15, 5, 26, 7, 9, 4, 33, 30, 12, 4, 10, 14, 6, 29, 20, 14, 15, 5, 17, 10, 3, 28, 40, 9, 5, 9, 42, 16, 27, 4, 14, 13, 22, 17, 18, 8, 19, 22, 11, 23, 27, 5
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Also, number of prime factors (with multiplicity) of the product P(n) of the composite numbers between n-th and (n+1)-th prime.
The number of elements in the (SFP) Smarandache Factor Partition of P(n) (product of composite numbers between successive primes) with maximum length.
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REFERENCES
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Amarnath Murthy, Generalization of Partition function, Introducing Smarandache Factor Partition. Smarandache Notions Journal, Vol. 11, 2000.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
M. L. Perez et al., eds., Smarandache Notions Journal
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FORMULA
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sum{A001222(k): A000040(n)<k<A000040(n+1)}. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 29 2002
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EXAMPLE
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a(6) = 8. prime(6) = 13, and the product of composite numbers between 13 and 17 is 14*15*16 = 2^5*3*5*7, with 8 prime factors.
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CROSSREFS
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Cf. A052297
Sequence in context: A029632 A089588 A014840 this_sequence A102780 A115025 A075428
Adjacent sequences: A077215 A077216 A077217 this_sequence A077219 A077220 A077221
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Nov 03 2002
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EXTENSIONS
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More terms and better description from Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 29 2002
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