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%I #22 Mar 08 2024 11:59:09
%S 53,68,117,222,321,1005,2587,4026,4185,4197,5722,5828,5961,8006,8376,
%T 11661,12369,12563,13583,14340,15367,16118,17842,18720,20543,25132,
%U 29395,30172,32667,36518,39915,40662,42425,42924,47843,49764,50040,50437,52314,53220
%N Numbers n such that sigma(n - 2) = sigma(n + 2).
%C Corresponding values of sigma(n - 2) = sigma(n + 2): 72, 144, 144, 504, 360, 1080, 3456, 7560, 4320, 5040, 15120, 11664, .... The first two values not divisible by 72 are for n = 21 and 23, a(n) = 15367 and 17842, sigma = 21120 and 41664. A search up to a(n) = 10^8 did not turn up any sigma not divisible by 24. - _Michael B. Porter_, Mar 28 2013
%H Donovan Johnson, <a href="/A223091/b223091.txt">Table of n, a(n) for n = 1..1000</a>
%e sigma(53 - 2) = sigma(53 + 2) = 72, sigma(68 - 2) = sigma(68 + 2) = 144, sigma(117 - 2) = sigma(117 + 2) = 144, sigma(222 - 2) = sigma(222 + 2) = 504, sigma(321 - 2) = sigma(321 + 2) = 360.
%t Select[Range[10000], DivisorSigma[1, # - 2] == DivisorSigma[1, # + 2] &] (* _Alonso del Arte_, Mar 23 2013 *)
%t Flatten[Position[Partition[DivisorSigma[1,Range[55000]],5,1],_?(#[[1]] == #[[5]]&),{1},Heads->False]]+2 (* _Harvey P. Dale_, Sep 14 2016 *)
%o (PARI) is(n)=sigma(n-2)==sigma(n+2) \\ _Charles R Greathouse IV_, Mar 17 2014
%Y Cf. A067135, A175876.
%K nonn
%O 1,1
%A _Irina Gerasimova_, Mar 22 2013
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