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A104149 Numbers n such that sigma(n+2) = sigma(n+1) + sigma(n). 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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

LINKS

Donovan Johnson and Giovanni Resta, Table of n, a(n) for n = 1..95 (terms < 4*10^12, first 50 terms from Donovan Johnson)

FORMULA

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

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

EXAMPLE

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).

MAPLE

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

for n from 1 to i do

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

od; end: A104149(10^9); # Paolo P. Lava, Apr 24 2013

MATHEMATICA

Select[Range@ 100000, DivisorSigma[1, # + 2] == DivisorSigma[1, # + 1] + DivisorSigma[1, #] &] (* Michael De Vlieger, Mar 23 2015 *)

PROG

(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

CROSSREFS

Sequence in context: A177410 A193486 A054948 * A113761 A054349 A182293

Adjacent sequences:  A104146 A104147 A104148 * A104150 A104151 A104152

KEYWORD

nonn,changed

AUTHOR

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

EXTENSIONS

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

STATUS

approved

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Last modified March 26 21:57 EDT 2015. Contains 255918 sequences.