OFFSET
1,1
COMMENTS
There are 34 terms up to 10^8. The abundance of odd terms (only 3 terms) is 6 (see also A087167). The abundance of even terms is 28, 496, 8128, and 33550336 (for 97364848). There exist deficient numbers whose abundance is a perfect number in absolute terms, e.g., 7, 29, 62.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..68
EXAMPLE
48 is a term as it is abundant and its abundance, sigma(48)-2*48 = 28, is the second perfect number.
MATHEMATICA
Select[Range[10^8], PerfectNumberQ[DivisorSigma[1, # ]-2#]&]
PROG
(PARI) for(n=1, 10^8, a=sigma(n)-2*n; a>0&&sigma(a)==2*a&&print1(n ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Waldemar Puszkarz, Mar 27 2018
STATUS
approved