A054903 Composite numbers n such that sigma(n)+6 = sigma(n+6), where sigma=A000203.

104, 147, 596, 1415, 4850, 5337, 370047, 1630622, 35020303, 120221396, 3954451796, 742514284703

Offset: 1

Author

Labos Elemer, May 23 2000

Keywords

• nonn
• more

Comments

Complement of A023201 with respect to A015914.

Intersection of A015914 and A018252.

Below 1000000 there are only 7 such composite numbers, compared with more than 16000 primes.

a(13) > 10^13. - Giovanni Resta, Jul 11 2013

Examples

			n=104, sigma(104)+6 = 210+6 = 216 = sigma(104+6) = sigma(110).
a(4) = 1415 = 5*283, 1415+6 = 1421 = 7*7*29:
sigma(1415) = 1+5+283+1415 = 1704,
sigma(1421) = 1+7+29+49+203+1421 = 1710 = sigma(1415)+6.
		

References

• J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 104, p. 37, Ellipses, Paris 2008.

Crossrefs

Cf. A015913-A015917, A023200-A023203, A046133, A001359, A054799.

Programs

PARI

forcomposite(n=9,1e7,if(sigma(n)+6==sigma(n+6),print1(n", "))) \\ Charles R Greathouse IV, Feb 14 2013

Extensions

More terms from Jud McCranie, May 25 2000

New definition from Reinhard Zumkeller, Jan 27 2009

Edited by N. J. A. Sloane, Jan 31 2009 at the suggestion of R. J. Mathar.

a(12) from Giovanni Resta, Jul 11 2013