A054799 Integers n such that sigma(n+2) = sigma(n) + 2, where sigma = A000203, the sum of divisors of n.

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

Offset: 1

Author

Labos Elemer, May 22 2000

Keywords

• nonn

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

Examples

			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.
		

References

• Sivaramakrishnan, R. (1989): Classical Theory of Arithmetical Functions., M.Dekker Inc., New York, Problem 12 in Chapter V., p. 81.

Crossrefs

Cf. A000203, A001359, A050507.

Programs

Mathematica

Select[Range[1500],DivisorSigma[1,#+2]==DivisorSigma[1,#]+2&] (* Jayanta Basu, May 01 2013 *)

PARI

is(n)=sigma(n+2)==sigma(n)+2 \\ Charles R Greathouse IV, Feb 13 2013