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 A054799 Integers n such that sigma(n+2) = sigma(n) + 2, where sigma = A000203, the sum of divisors of n. 16
 3, 5, 11, 17, 29, 41, 59, 71, 101, 107, 137, 149, 179, 191, 197, 227, 239, 269, 281, 311, 347, 419, 431, 434, 461, 521, 569, 599, 617, 641, 659, 809, 821, 827, 857, 881, 1019, 1031, 1049, 1061, 1091, 1151, 1229, 1277, 1289, 1301, 1319, 1427, 1451, 1481, 1487 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Only 3 composite numbers are known: 434, 8575, 8825. This sequence is the union of A050507 and A001359. 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 REFERENCES Sivaramakrishnan, R. (1989): Classical Theory of Arithmetical Functions., M.Dekker Inc., New York, Problem 12 in Chapter V., p. 81. LINKS EXAMPLE 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. MATHEMATICA Select[Range[1500], DivisorSigma[1, #+2]==DivisorSigma[1, #]+2&] (* Jayanta Basu, May 01 2013 *) PROG (PARI) is(n)=sigma(n+2)==sigma(n)+2 \\ Charles R Greathouse IV, Feb 13 2013 CROSSREFS Cf. A000203, A001359, A050507. Sequence in context: A069233 A063700 A078859 * A093326 A001359 A096292 Adjacent sequences:  A054796 A054797 A054798 * A054800 A054801 A054802 KEYWORD nonn,changed AUTHOR Labos Elemer, May 22 2000 STATUS approved

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