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%I #11 Jan 06 2024 21:52:20
%S 4,7,9,10,12,19,27,31,33,45,51,61,67,68,73,76,85,93,114,141,153,154,
%T 162,164,174,186,187,190,201,208,211,213,217,220,230,236,242,243,245,
%U 258,261,266,267,273,277,290,291,294,301,308,337,342,354,355,356,364,367
%N A positive integer n is included if (d(n),d(n+1),d(n+2)) is a permutation of three integers in arithmetic progression, where d(n) = the number of divisors of n.
%H Harvey P. Dale, <a href="/A175149/b175149.txt">Table of n, a(n) for n = 1..1000</a>
%e d(10) = 4, d(11) = 2, and d(12) = 6. Now, (4,2,6) is a permutation of (2,4,6), which are three integers in arithmetic progression because 4-2 = 6-4. So 10 is included in the sequence.
%t Position[Partition[DivisorSigma[0,Range[400]],3,1],_?(Length[Union[ Differences[ Sort[#]]]]==1&),1,Heads->False]//Flatten (* _Harvey P. Dale_, Dec 09 2017 *)
%Y Cf. A000005.
%K nonn
%O 1,1
%A _Leroy Quet_, Feb 24 2010
%E Extended by _Ray Chandler_, Mar 03 2010