

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

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



