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 A054432 a(n) = Sum_{1<=k<=n,GCD(k,n)=1} 2^(k-1). 14
 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, 3679302363, 5726557525 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS For n>0, numbers formed by interpreting the reduced residue set of n (the rows of triangle A054431) as binary numbers. LINKS Robert Israel, Table of n, a(n) for n = 1..2658 FORMULA M * V, where M = A054521 is an infinite lower triangular matrix and V = [1, 2, 4, 8...] is a vector. - Gary W. Adamson, Jan 13 2007 a(4*n) = (2^(2*n) + 1)*a(2*n) [think how the reduced residue set of the numbers of the form 4n are formed] For all primes p and integers e > 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, Aug 15 2002 EXAMPLE For n=6 we have k = 1 and 5 and then 2^0 + 2^4 = 17 = a(6). MAPLE 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; MATHEMATICA f[n_] := Sum[2^k, {k, Select[ Range@ n, GCD[#, n] == 1 &] - 1}]; Array[f, 35] (* Robert G. Wilson v, Jul 21 2014 *) PROG (PARI) a(n) = sum(k=1, n, if (gcd(k, n)==1, 2^(k-1), 0)); \\ Michel Marcus, Jul 20 2014 (PARI) a(n) = subst(Polrev(vector(n, i, gcd(n, i)==1)), x, 2); \\ Michel Marcus, Jul 21 2014 CROSSREFS Cf. A054431, A054433, A001317, A054521. Sequence in context: A053576 A197818 A077406 * A016043 A077403 A002962 Adjacent sequences:  A054429 A054430 A054431 * A054433 A054434 A054435 KEYWORD nonn AUTHOR EXTENSIONS Edited by N. J. A. Sloane, Jul 03 2008 at the suggestion of R. J. Mathar More terms from Michel Marcus, Jul 20 2014 STATUS approved

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Last modified December 11 11:30 EST 2018. Contains 318049 sequences. (Running on oeis4.)