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

1,1

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

Links

Table of n, a(n) for n=1..11.

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A009405 A009839 A190066 * A071767 A161461 A162297

Adjacent sequences: A335250 A335251 A335252 * A335254 A335255 A335256

Keyword

nonn,more

Author

Amiram Eldar, May 28 2020

Status

approved