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
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)
Programs
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Magma
[#Divisors(n):n in [1..4000000]| SumOfDivisors(n) eq SumOfDivisors(n+1)]; // Marius A. Burtea, Sep 07 2019
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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 *) -
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
Formula
a(n) = tau(A002961(n)).
Extensions
More terms from Naohiro Nomoto, Mar 16 2001