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A175149
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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.
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1
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4, 7, 9, 10, 12, 19, 27, 31, 33, 45, 51, 61, 67, 68, 73, 76, 85, 93, 114, 141, 153, 154, 162, 164, 174, 186, 187, 190, 201, 208, 211, 213, 217, 220, 230, 236, 242, 243, 245, 258, 261, 266, 267, 273, 277, 290, 291, 294, 301, 308, 337, 342, 354, 355, 356, 364, 367
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OFFSET
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1,1
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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Position[Partition[DivisorSigma[0, Range[400]], 3, 1], _?(Length[Union[ Differences[ Sort[#]]]]==1&), 1, Heads->False]//Flatten (* Harvey P. Dale, Dec 09 2017 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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