A359135 Decimal expansion of the aliquot constant (negated).

0, 3, 3, 2, 5, 9, 4, 8, 0, 8, 0, 0, 9

Offset

0,2

Comments

This is the geometric mean of log(s(2n)/2n) where s(n) = A001065(n) = sigma(n) - n is the sum of aliquot parts function. As it is slightly negative, s(2n) is 'on average' smaller than 2n.

References

J.-M. De Koninck, Review of "Carl Pomerance, The aliquot constant, after Bosma and Kane, Q. J. Math. 69 (2018), no. 3, 915-930", Math Review MR3859214.

Carl Pomerance, The aliquot constant, after Bosma and Kane, The Quarterly Journal of Mathematics, Volume 69, Issue 3, September 2018, Pages 915-930, https://doi.org/10.1093/qmath/hay005 [From journal website]

Carl Pomerance, Email to N. J. A. Sloane, Jan 18 2023

Links

Table of n, a(n) for n=0..12.

W. Bosma and B. Kane, The aliquot constant, arXiv:0912.3660 [math.NT], 2009.

W. Bosma and B. Kane, The aliquot constant, Quarterly Journal of Mathematics 63 (2012), pp. 309-323.

Carl Pomerance, The aliquot constant, after Bosma and Kane, "aliconstantpaperrevised.pdf", Dec 28 2017. [Probably gives an incorrect value]

Carl Pomerance, The aliquot constant, after Bosma and Kane, "aliconstantpaper2.pdf", Jan 20 2018.

Example

The constant is between -0.03325948080092 and -0.03325948080094. - Carl Pomerance, Jan 18 2023

Crossrefs

Sequence in context: A083343 A360736 A292527 * A359484 A186111 A186813

Adjacent sequences: A359132 A359133 A359134 * A359136 A359137 A359138

Keyword

nonn,cons,more

Author

N. J. A. Sloane, Jan 16 2023

Status

approved