A069085 Abundant numbers n such that n = sigma(k) - 2k, where k = sigma(n) - 2n.

120, 672, 45840, 51168, 523776, 459818240, 1476304896, 51001180160

Offset: 1

Author

Naohiro Nomoto, Apr 05 2002

Keywords

• more
• nonn

Comments

All triply perfect numbers (A005820) are in the sequence, as are 45840 and 51168. Are there any other terms?

a(8) > 10^10. - Donovan Johnson, Apr 22 2012

a(9) > 1.3*10^11. - Giovanni Resta, Jun 06 2016

Examples

			sigma(45840) - 2*45840 = 51168 and sigma(51168) - 2*51168 = 45840, so 45840 and 51168 are in the sequence.
		

Crossrefs

Cf. A005820.

Programs

Mathematica

For[n=1, True, n++, k=DivisorSigma[1, n]-2n; If[k>0&&DivisorSigma[1, k]-2k==n, Print[n]]]

Extensions

Edited by Dean Hickerson, Apr 11 2002

a(7) from Donovan Johnson, Apr 22 2012

a(8) from Giovanni Resta, Jun 06 2016