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
EXAMPLE
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
KEYWORD
nonn,more
AUTHOR
Amiram Eldar, May 28 2020
STATUS
approved