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%I #17 Apr 07 2024 09:10:14
%S 48,2002,2632,4540,5170,6952,8925,29056,32445,32980,88330,133042,
%T 174856,189472,280228,442365,518368,566752,892552,1266952,2030368,
%U 2052256,2218450,3959752,4120672,4558936,5568448,9071752,15921112,38551936,65969536,70114936,88149352,97364848
%N Abundant numbers whose abundance is a perfect number.
%C 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.
%H Amiram Eldar, <a href="/A301859/b301859.txt">Table of n, a(n) for n = 1..68</a>
%e 48 is a term as it is abundant and its abundance, sigma(48)-2*48 = 28, is the second perfect number.
%t Select[Range[10^8], PerfectNumberQ[DivisorSigma[1,# ]-2#]&]
%o (PARI) for(n=1,10^8, a=sigma(n)-2*n; a>0&&sigma(a)==2*a&&print1(n ","))
%Y Cf. A005101 (abundant numbers), A033880 (abundance), A000396 (perfect numbers), A087167, A088834, A088012, A077374 (sequences related to the odd terms of this sequence).
%K nonn,changed
%O 1,1
%A _Waldemar Puszkarz_, Mar 27 2018
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