A083795 Numbers n such that n and n-1 have the same number of divisors. Numbers not included in A083794.

3, 15, 22, 27, 34, 35, 39, 45, 58, 76, 86, 87, 94, 95, 99, 105, 117, 119, 123, 134, 136, 142, 143, 146, 148, 159, 172, 178, 190, 202, 203, 206, 214, 215, 218, 219, 231, 232, 243, 244, 245, 254, 286, 297, 299, 302, 303, 327, 333, 335, 345, 375, 376, 382, 388

Offset

1,1

Comments

Also numbers n such that sigma_0(n+1) * sigma_0(n) / (sigma_0(n+1) + sigma_0(n)) = c, c an integer. - Ctibor O. Zizka, Nov 01 2008

Heath-Brown proved that this sequence is infinite. Hildebrand and Erdős, Pomerance, & Sárközy show that n sqrt(log log n) << a(n) << n (log log n)^3, where << is Vinogradov notation. - Charles R Greathouse IV, Oct 20 2013

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

P. Erdős, On a problem of Chowla and some related problems, Proc. Cambridge Philos. Soc. 32 (1936), pp. 530-540.

P. Erdős, C. Pomerance, and A. Sárközy, On locally repeated values of certain arithmetic functions, II, Acta Math. Hungarica 49 (1987), pp. 251-259. [alternate link]

D. R. Heath-Brown, The divisor function at consecutive integers, Mathematika 31 (1984), pp. 141-149.

Adolf Hildebrand, The divisor function at consecutive integers, Pacific J. Math. 129:2 (1987), pp. 307-319.

Maple

with(numtheory): for n from 3 to 10^3 do if tau(n) = tau(n-1) then printf(`%d, `, n) fi: od:

Mathematica

SequencePosition[DivisorSigma[0, Range[400]], {x_, x_}][[All, 2]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Apr 09 2019 *)

Prog

(PARI) is(n)=n>2 && numdiv(n)==numdiv(n-1) \\ Charles R Greathouse IV, Jul 21 2015

Crossrefs

Cf. A083794.

Sequence in context: A276804 A009057 A289712 * A083793 A324127 A083934

Adjacent sequences: A083792 A083793 A083794 * A083796 A083797 A083798

Keyword

nonn

Author

Amarnath Murthy, May 07 2003

Extensions

Corrected and extended by James A. Sellers, May 19 2003

Status

approved