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%I #57 Feb 18 2024 08:22:02
%S 5,8,41,56,946,5186,6874,8104,17386,27024,84026,167786,2667584,
%T 4921776,27914146,505235234,3238952914,73600829714,455879783074,
%U 528080296234,673223621664,4054397778846,4437083907194,4869434608274,6904301600914,7738291969456
%N Numbers that are equal to the sum of their anti-divisors.
%C See A066272 for definition of anti-divisor.
%H Jon Perry, <a href="https://web.archive.org/web/20060923020024/http://www.users.globalnet.co.uk/~perry/maths/antiperfect.htm">Anti-perfects, anti-amicables and other records</a>.
%e n=5186, the anti-divisor sum: 3+4+11+23+41+253+451+943+3457 = 5186.
%o (Python)
%o from sympy import divisors
%o A073930 = [n for n in range(1,10**5) if sum([2*d for d in divisors(n) if n > 2*d and n % (2*d)] + [d for d in divisors(2*n-1) if n > d >=2 and n % d] + [d for d in divisors(2*n+1) if n > d >=2 and n % d]) == n] # _Chai Wah Wu_, Aug 14 2014
%o (PARI) sad(n) = vecsum(select(t->n%t && t<n, concat(concat(divisors(2*n-1), divisors(2*n+1)), 2*divisors(n)))); \\ A066417
%o isok(n) = sad(n) == n; \\ _Michel Marcus_, Oct 12 2019
%Y Cf. A066417, A192272.
%K nonn,more
%O 1,1
%A _Jason Earls_, Sep 03 2002
%E Two more terms from _Lior Manor_ Mar 03 2004
%E a(18) from _Donovan Johnson_, Jun 19 2010
%E a(19)-a(21) by _Jud McCranie_, Aug 31 2019
%E a(22)-a(26) by _Jud McCranie_, Oct 10 2019
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