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A053249
Number of divisors of n such that n and n+1 have the same sum of divisors.
10
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
KEYWORD
nonn,nice
AUTHOR
Asher Auel, Jan 11 2000
EXTENSIONS
More terms from Naohiro Nomoto, Mar 16 2001
STATUS
approved