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A104149 Numbers n such that sigma(n+2) = sigma(n+1) + sigma(n). 3

%I

%S 1,2,22,1966,3262,5014,60454,1016506,4420162,12055510,14365606,

%T 25726726,27896422,66562306,72764734,98734966,175186654,224868310,

%U 253694926,288657202,386668342,421575406,504737746,630645454,1493547998,1653797794,2120325010,2221315150

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

%C Apparently all terms >1 are even. - _Zak Seidov_, Mar 23 2015

%C 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

%H Donovan Johnson and Giovanni Resta, <a href="/A104149/b104149.txt">Table of n, a(n) for n = 1..112</a> (terms < 10^13, first 50 terms from Donovan Johnson)

%F a(n) = A065900(n) - 2. - _R. J. Mathar_, Aug 19 2010

%F a(n) = A076530(n) - 1. - _M. F. Hasler_, Aug 19 2010

%e sigma(22) = 1+2+11+22 = 36.

%e sigma(23) = 1+23 = 24.

%e sigma(24) = 1+2+3+4+6+8+12+24 = 60.

%e sigma(24) = sigma(23) + sigma(22).

%p with(numtheory); A104149:=proc(i) local n;

%p for n from 1 to i do

%p if sigma(n+2)=sigma(n+1)+sigma(n) then print(n); fi;

%p od; end: A104149(10^9); # _Paolo P. Lava_, Apr 24 2013

%t Select[Range@ 100000, DivisorSigma[1, # + 2] == DivisorSigma[1, # + 1] + DivisorSigma[1, #] &] (* _Michael De Vlieger_, Mar 23 2015 *)

%t 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 *)

%o (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 */

%o (MAGMA) [n: n in [1..2*10^6] | SumOfDivisors(n+2) eq (SumOfDivisors(n+1)+SumOfDivisors(n))]; // _Vincenzo Librandi_, Mar 24 2015

%K nonn

%O 1,2

%A Neven Juric (neven.juric(AT)apis-it.hr), Aug 16 2010

%E More terms from _Zak Seidov_ and _R. J. Mathar_, Aug 19 2010

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Last modified March 2 12:26 EST 2021. Contains 341750 sequences. (Running on oeis4.)