

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
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OFFSET

1,1


COMMENTS

Below 1000000 only 3 composite numbers were found: 434, 8575, 8825. This sequence is the union of A050507 and A001359.


REFERENCES

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


LINKS

Table of n, a(n) for n=1..51.


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


AUTHOR

Labos Elemer, May 22 2000


STATUS

approved



