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A088837 Numerator of sigma(2*n)/sigma(n). Denominator see in A038712. 9
3, 7, 3, 15, 3, 7, 3, 31, 3, 7, 3, 15, 3, 7, 3, 63, 3, 7, 3, 15, 3, 7, 3, 31, 3, 7, 3, 15, 3, 7, 3, 127, 3, 7, 3, 15, 3, 7, 3, 31, 3, 7, 3, 15, 3, 7, 3, 63, 3, 7, 3, 15, 3, 7, 3, 31, 3, 7, 3, 15, 3, 7, 3, 255, 3, 7, 3, 15, 3, 7, 3, 31, 3, 7, 3, 15, 3, 7, 3, 63, 3, 7, 3, 15, 3, 7, 3, 31, 3, 7, 3, 15, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

In general sigma(2^k*n) / sigma(n) = ((2^k*n) XOR (2^k*n-1)) / (n XOR (n-1)), see link. Jon Maiga, Dec 10 2018

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..16384

J. Maiga, Efficient computation of ratios between divisor sums, 2018.

FORMULA

a(n) = 4*2^A007814(n)-1 = 4*A006519(n)-1 = A059159(n)-1 = 2*A038712(n) + 1.

a((2*n-1)*2^p) = 2^(p+2)-1, p >= 0 and n >= 1. - Johannes W. Meijer, Feb 09 2013

a(n) = (2n) XOR (2n-1). - Jon Maiga, Dec 10 2018

MAPLE

nmax:=93: for p from 0 to ceil(simplify(log[2](nmax))) do for n from 1 to ceil(nmax/(p+2)) do a((2*n-1)*2^p) := 2^(p+2)-1 od: od: seq(a(n), n=1..nmax); # Johannes W. Meijer, Feb 09 2013

MATHEMATICA

k=2; Table[Numerator[DivisorSigma[1, k*n]/DivisorSigma[1, n]], {n, 1, 128}]

Table[BitXor[2*n, 2*n - 1], {n, 128}] (* Jon Maiga, Dec 10 2018 *)

PROG

(PARI) A088837(n) = numerator(sigma(n<<1)/sigma(n)); \\ Antti Karttunen, Nov 01 2018

CROSSREFS

Cf. A088838, A088839, A088840, A080278, A220466.

Sequence in context: A316255 A096385 A205723 * A201385 A186107 A282160

Adjacent sequences:  A088834 A088835 A088836 * A088838 A088839 A088840

KEYWORD

easy,nonn,frac

AUTHOR

Labos Elemer, Nov 04 2003

STATUS

approved

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Last modified January 20 12:19 EST 2019. Contains 319330 sequences. (Running on oeis4.)