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Search: id:A118657
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| A118657 |
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a(n) = Sum_[k unrelated to n and k<n] a(k) = Sum_[k < n such that GCD(k,n) != 1 and k does not divide n ] a(k); a(1) = a(2) = a(3) = 1. |
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| 1, 1, 1, 0, 0, 1, 0, 1, 1, 3, 0, 5, 0, 10, 10, 19, 0, 39, 0, 85, 66, 164, 0, 397, 98
(list; graph; listen)
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OFFSET
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1,10
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COMMENT
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Primes include a(10) = 3, a(12) = 5, a(16) = 19, a(24) = 397. a(n) is unrelated to n for a(14) = 10, a(15) = 10, a(18) = 39, a(20) = 85, a(21) = 66, a(22) = 164.
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FORMULA
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For primes p>3, a(p) = 0.
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EXAMPLE
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a(4) = 0 as A045763(4) = 0, i.e. there are no numbers less than 4 which are unrelated to 4.
a(6) = 1 because 4 is the only number less than 6 which is unrelated to 6, so a(6) = a(4) = 1.
a(10) = a(4) + a(6) + a(8) = 1 + 1 + 1 = 3.
a(12) = a(8) + a(9) + a(10) = 1 + 1 + 3 = 5.
a(24) = a(9) + a(10) + a(14) + a(15) + a(16) + a(18) + a(20) + a(21) + a(22) = 1 + 3 + 10 + 10 + 19 + 39 + 85 + 66 + 164 = 397.
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CROSSREFS
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See also A045763 = number of numbers "unrelated to n": m<n such that m is neither a divisor of n nor relatively prime to n; A118314 = Divisor-indexed recurrence; A118418 = Relative-prime-indexed recurrence; A111356 = numbers n such that the number of numbers "unrelated to n" is itself unrelated to n.
Cf. A070297.
Sequence in context: A049283 A051704 A049689 this_sequence A047760 A050925 A086696
Adjacent sequences: A118654 A118655 A118656 this_sequence A118658 A118659 A118660
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), May 18 2006
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EXTENSIONS
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Edited by njas, Dec 03 2006
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