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

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

Offset: 1

Author

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

Keywords

• nonn

Comments

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

Examples

			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).
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..112 (terms < 10^13; first 50 terms from Donovan Johnson)

Programs

Magma

[n: n in [1..2*10^6] | SumOfDivisors(n+2) eq (SumOfDivisors(n+1)+SumOfDivisors(n))]; // Vincenzo Librandi, Mar 24 2015

Mathematica

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 *)

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 */

Formula

a(n) = A065900(n) - 2. - R. J. Mathar, Aug 19 2010

a(n) = A076530(n) - 1. - M. F. Hasler, Aug 19 2010

Extensions

More terms from Zak Seidov and R. J. Mathar, Aug 19 2010