A053249 Number of divisors of n such that n and n+1 have the same sum of divisors.

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

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10135 (from the b-file 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]] (* Jean-François 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(n-1))); 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, Jan 11 2000

Extensions

More terms from Naohiro Nomoto, Mar 16 2001

Status

approved