A335253 Numbers k such that the abundance (A033880) of k is equal to the deficiency (A033879) of k+2.

12, 76, 488, 556, 1100, 1430, 2408, 8896, 538208, 13685780, 962402768

Offset: 1

Author

Amiram Eldar, May 28 2020

Keywords

• nonn
• more

Comments

Equivalently, k and k+2 have the same absolute value of abundance (or deficiency) with opposite signs.

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

a(12) > 10^11, if it exists.

a(12) > 10^13, if it exists. - Giovanni Resta, May 30 2020

Examples

			12 is a term since A033880(12) = sigma(12) - 2*12 = 28 - 24 = 4, and A033879(14) = 2*14 - sigma(14) = 28 - 24 = 4.
		

Crossrefs

Cf. A000203, A001065, A033879, A033880, A330901, A335254.

Programs

Mathematica

ab[n_] := DivisorSigma[1, n] - 2*n; Select[Range[10^5], ab[#] == -ab[# + 2] &]

PARI

isok(k) = sigma(k) + sigma(k+2) == 4*k+4; \\ Michel Marcus, May 29 2020