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Numbers n such that sigma(n) + sigma(n+3) = sigma(n+1) + sigma(n+2).
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%I #13 Feb 11 2014 19:05:32

%S 2012,2096,15892,17888,39916,102784,141008,146227,482144,487865,

%T 1321312,1887008,2749057,3513881,7141158,16767172,17503912,28122834,

%U 30534728,37453779,42140437,60994100,67777337,78251933,113091820,113768920,129868059,199240914,240859196,302897372

%N Numbers n such that sigma(n) + sigma(n+3) = sigma(n+1) + sigma(n+2).

%C Each term of the sequence marks the start of four consecutive sigma-values for which the sum of the means equals the sum of the extremes.

%H Giovanni Resta, <a href="/A076666/b076666.txt">Table of n, a(n) for n = 1..90</a> (terms < 4*10^12)

%e sigma(2012) + sigma(2015) = 3528 + 2688 = 6216; sigma(2013) + sigma(2014) = 2976 + 3240 = 6216, so 2012 is a term of the sequence.

%t Select[Range[10^5], DivisorSigma[1, # ] + DivisorSigma[1, # + 3] == DivisorSigma[1, # + 1] + DivisorSigma[1, # + 2] &]

%Y Cf. A000203, A055574, A065900, A073500, A099632, A226361, A226475.

%K nonn

%O 1,1

%A _Joseph L. Pe_, Oct 25 2002

%E a(6)-a(26) from _Donovan Johnson_, Feb 01 2009

%E a(27)-a(30) from _Alex Ratushnyak_, Jun 29 2013