

A053249


Number of divisors of n such that n and n+1 have the same sum of divisors.


9



4, 4, 8, 8, 12, 8, 8, 4, 6, 12, 10, 4, 16, 12, 8, 8, 8, 12, 16, 8, 8, 16, 16, 16, 16, 8, 16, 8, 16, 4, 16, 16, 16, 12, 24, 12, 16, 8, 16, 16, 8, 16, 16, 12, 16, 16, 16, 16, 12, 12, 12, 16, 16, 40, 16, 16, 32, 12, 24, 32, 24, 16, 16, 24, 24, 4, 24, 16, 64, 24, 16, 8, 16, 16, 16, 24, 32, 32, 20, 16
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OFFSET

1,1


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10135 (from the bfile at A002961; terms 1..4804 from T. D. Noe)


FORMULA

a(n) = tau(A002961(n))


MATHEMATICA

Reap[ Do[ If[ DivisorSigma[1, n] == DivisorSigma[1, n + 1], tau = DivisorSigma[0, n]; Print[{n, tau}]; Sow[tau]], {n, 1, 4*10^6}]][[2, 1]] (* JeanFrançois Alcover, Oct 08 2012 *)
DivisorSigma[0, #]&/@Flatten[Position[Partition[DivisorSigma[1, Range[ 4000000]], 2, 1], _?(First[#] == Last[#]&), {1}, Heads>False]] (* Harvey P. Dale, Jul 04 2014 *)
DivisorSigma[0, #]&/@(SequencePosition[DivisorSigma[1, Range[4000000]], {x_, x_}][[All, 1]]) (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 25 2019 *)


PROG

(PARI) do(lim)=my(v=List(), k=1, t); for(n=2, lim, t=sigma(n); if(t==k, listput(v, numdiv(n1))); k=t); Vec(v) \\ Charles R Greathouse IV, Feb 08 2017
(MAGMA) [#Divisors(n):n in [1..4000000] SumOfDivisors(n) eq SumOfDivisors(n+1)]; // Marius A. Burtea, Sep 07 2019


CROSSREFS

Cf. A000203, A000005, A002961, A053215, A054002, A054003.
Sequence in context: A105675 A196054 A292135 * A071339 A146890 A168273
Adjacent sequences: A053246 A053247 A053248 * A053250 A053251 A053252


KEYWORD

nonn,nice


AUTHOR

Asher Auel (asher.auel(AT)reed.edu), Jan 11 2000


EXTENSIONS

More terms from Naohiro Nomoto, Mar 16 2001


STATUS

approved



