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A083795 Numbers n such that n and n-1 have the same number of divisors. Numbers not included in A083794. 5
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 4 16:59 EDT 2021. Contains 346454 sequences. (Running on oeis4.)