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Search: id:A100107
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| A100107 |
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Inverse Moebius transform of Lucas numbers (A000032) 1,3,4,7,11,.. |
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+0
4
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| 1, 4, 5, 11, 12, 26, 30, 58, 81, 138, 200, 355, 522, 876, 1380, 2265, 3572, 5880, 9350, 15272, 24510, 39806, 64080, 104084, 167773, 271968, 439285, 711530, 1149852, 1862022, 3010350, 4873112, 7881400, 12755618, 20633280, 33391491, 54018522
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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a(n) = SUM[d|n]L(d) = a(n) = SUM[d|n]A000032(d).
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EXAMPLE
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a(2) = 4 because the prime 2 is divisible only by 1 and 2, so L(1) + L(2) = 1 + 3 = 4.
a(3) = 5 because the prime 3 is divisible only by 1 and 3, so L(1) + L(3) = 1 + 4 = 5.
a(4) = 11 because the semiprime 4 is divisible only by 1, 2, 4, so L(1) + L(2) + L(4) = 1 + 3 + 7 = 11.
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MAPLE
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with(numtheory): with(combinat): a:=proc(n) local div: div:=divisors(n): sum(2*fibonacci(div[j]+1)-fibonacci(div[j]), j=1..tau(n)) end: seq(a(n), n=1..42); (Deutsch)
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CROSSREFS
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Cf. A000032, A007435, A100279.
Sequence in context: A069820 A027708 A047374 this_sequence A066828 A163098 A039006
Adjacent sequences: A100104 A100105 A100106 this_sequence A100108 A100109 A100110
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KEYWORD
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nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Dec 26 2004
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 31 2005
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