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A104149
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Numbers k such that sigma(k+2) = sigma(k+1) + sigma(k).
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5
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1, 2, 22, 1966, 3262, 5014, 60454, 1016506, 4420162, 12055510, 14365606, 25726726, 27896422, 66562306, 72764734, 98734966, 175186654, 224868310, 253694926, 288657202, 386668342, 421575406, 504737746, 630645454, 1493547998, 1653797794, 2120325010, 2221315150
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OFFSET
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1,2
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COMMENTS
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Apparently all terms > 1 are even. - Zak Seidov, Mar 23 2015
For n <= 95, no a(n) is divisible by 3; a(2), a(25) and a(57) == 2 (mod 3), the rest == 1 (mod 3). - Robert Israel, Mar 23 2015
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LINKS
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FORMULA
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EXAMPLE
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sigma(22) = 1+2+11+22 = 36.
sigma(23) = 1+23 = 24.
sigma(24) = 1+2+3+4+6+8+12+24 = 60.
sigma(24) = sigma(23) + sigma(22).
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MATHEMATICA
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Select[Range@ 100000, DivisorSigma[1, # + 2] == DivisorSigma[1, # + 1] + DivisorSigma[1, #] &] (* Michael De Vlieger, Mar 23 2015 *)
Position[Partition[DivisorSigma[1, Range[3*10^7]], 3, 1], _?(#[[1]]+#[[2]]==#[[3]]&), 1, Heads->False]//Flatten (* The program generates the first 13 terms *) (* Harvey P. Dale, May 08 2018 *)
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PROG
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(PARI) s1=1; s2=3; for(n=1, 10^8, s3=sigma(n+2); if(s3==s1+s2, print1(n ", ")); s1=s2; s2=s3) /* Donovan Johnson, Apr 08 2013 */
(Magma) [n: n in [1..2*10^6] | SumOfDivisors(n+2) eq (SumOfDivisors(n+1)+SumOfDivisors(n))]; // Vincenzo Librandi, Mar 24 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Neven Juric (neven.juric(AT)apis-it.hr), Aug 16 2010
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EXTENSIONS
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STATUS
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approved
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