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%I #17 Nov 14 2014 09:36:04
%S 3,5,11,17,29,41,59,71,101,107,137,149,179,191,197,227,239,269,281,
%T 311,347,419,431,434,461,521,569,599,617,641,659,809,821,827,857,881,
%U 1019,1031,1049,1061,1091,1151,1229,1277,1289,1301,1319,1427,1451,1481,1487
%N Integers n such that sigma(n+2) = sigma(n) + 2, where sigma = A000203, the sum of divisors of n.
%C Only 3 composite numbers are known: 434, 8575, 8825. This sequence is the union of A050507 and A001359.
%C The terms are also the solutions of A001065(x) = A001065(x+2), where A001065(n) is the sum of proper divisors of n. - _Michel Marcus_, Nov 14 2014
%D Sivaramakrishnan, R. (1989): Classical Theory of Arithmetical Functions., M.Dekker Inc., New York, Problem 12 in Chapter V., p. 81.
%e n = 434, divisors = {1, 2, 7, 14, 31, 62, 217, 434}, sigma(434) = 768, sigma(436) = 770; n = 8575, divisors = {1, 5, 7, 25, 35, 49, 175, 245, 343, 1225, 1715, 8575}, sigma(8575) = 12400, sigma(8577) = 12402; n = 8825, divisors = {1, 5, 25, 353, 1765, 8825}, sigma(8525) = 10974, sigma(8527) = 10976.
%t Select[Range[1500],DivisorSigma[1,#+2]==DivisorSigma[1,#]+2&] (* _Jayanta Basu_, May 01 2013 *)
%o (PARI) is(n)=sigma(n+2)==sigma(n)+2 \\ _Charles R Greathouse IV_, Feb 13 2013
%Y Cf. A000203, A001359, A050507.
%K nonn
%O 1,1
%A _Labos Elemer_, May 22 2000