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Search: id:A054432
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| A054432 |
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Sum {1<=k<=n,GCD(k,n)=1}, 2^(k-1). |
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+0
13
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| 1, 1, 3, 5, 15, 17, 63, 85, 219, 325, 1023, 1105, 4095, 5397, 13515, 21845, 65535, 70737, 262143, 333125, 890523, 1397077, 4194303, 4527185, 16236015, 22365525, 57521883, 88429845, 268435455, 272962625, 1073741823, 1431655765
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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For n>0, numbers formed by interpreting the reduced residue set of n (the rows of triangle A054431) as binary numbers.
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FORMULA
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M * V, where M = A054521 is an infinite lower triangular matrix, and V = [1, 2, 4, 8...] is a vector. - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 13 2007
a(n) = rrs2bincode(n+1) # Starting from n = 1.
a(4n-1) = (2^2n + 1)*a(2n-1) [think how the reduced residue set of the numbers of the form 4n are formed]
For all p's prime, and e's integer > 1, A054432[p^e] = A019320[p^e]*(((2^(p^(e-1)))-1)* ((2^(p-1))-1))/((2^p)-1)
a(n-1) = Sum_{k=1..n, gcd(n, k) = 1} 2^(k-1). - Vladeta Jovovic (vladeta(AT)Eunet.yu), Aug 15 2002
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EXAMPLE
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For n=6 we have k = 1 and 5, and then 2^0 + 2^4 = 17 = a(6).
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MAPLE
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rrs2bincode := proc(n) local i, z; z := 0; for i from 1 to n-1 do z := z*2; if (1 = igcd(n, i)) then z := z + 1; fi; od; RETURN(z); end;
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CROSSREFS
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Cf. A054431, A054433, A001317, A054521.
Sequence in context: A001317 A053576 A077406 this_sequence A016043 A077403 A018374
Adjacent sequences: A054429 A054430 A054431 this_sequence A054433 A054434 A054435
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen
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EXTENSIONS
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Edited by njas, Jul 03 2008 at the suggestion of R. J. Mathar
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