A335255 Numbers k such that ab(k) + ab(k+1) + ab(k+2) = 0, where ab(k) is the abundance of k (A033880).

5829840, 3414097920, 39339578248

Offset: 1

Author

Amiram Eldar, May 28 2020

Keywords

• nonn
• hard
• bref
• more

Comments

Equivalently, s(k) + s(k+1) + s(k+2) = k + (k+1) + (k+2), where s(k) is the sum of proper divisors of k (A001065).

a(4) > 10^11, if it exists.

a(4) > 10^13, if it exists. - Giovanni Resta, May 30 2020

Examples

			5829840 is a term since ab(5829840) + ab(5829841) + ab(5829842) = 8428320 - 5513402 - 2914918 = 0.
		

Crossrefs

Cf. A000203, A001065, A033880, A335254.

Programs

Mathematica

s[n_] := DivisorSigma[1, n] - n; Select[Range[6 * 10^6], s[#] + s[# + 1] + s[# + 2] == 3*# + 3 &]