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%I #41 Dec 11 2017 02:45:06
%S 0,0,0,0,0,6,0,0,0,0,0,6,0,0,0,0,0,6,0,0,0,0,0,6,0,0,0,28,0,6,0,0,0,0,
%T 0,6,0,0,0,0,0,6,0,0,0,0,0,6,0,0,0,0,0,6,0,28,0,0,0,6,0,0,0,0,0,6,0,0,
%U 0,0,0,6,0,0,0,0,0,6,0,0,0,0,0,34,0,0,0,0,0,6,0,0,0,0,0,6,0,0,0,0,0,6,0,0,0,0,0,6,0,0,0,28,0,6
%N Sum of the perfect divisors of n.
%C Sum of divisors d of n with sigma(d) = 2*d.
%C Unless an odd perfect number exists, a(n) = 0 whenever n is odd.
%C If no odd perfect numbers exist: If n is 6 mod 12 then a(n) = 6, if n is 1, 2, 3, 5, 7, 9, 10, or 11 mod 12 then a(n) = 0.
%C The first occurrence of three nonzero values at three consecutive even indices is a(1984) = 496, a(1986) = 6, a(1988) = 28.
%C Records are at n = 6, 28, 84, 496, 1488, 3472, 8128, 24384, 56896, 170688, 251968, 755904, 1763776, 5291328, 33550336, 100651008, 234852352, 704557056, 1040060416, 3120181248, 4260892672, .... - _Charles R Greathouse IV_, Jan 16 2013
%C A185351 gives the distinct values of this sequence (or numbers in the range of the sum of perfect divisors function) in ascending order. - _Timothy L. Tiffin_, Jul 13 2016
%C Fixed points: a(n) = n if and only if n is a perfect number (A000396). - _Timothy L. Tiffin_, Jul 14 2016
%H G. C. Greubel, <a href="/A187794/b187794.txt">Table of n, a(n) for n = 1..10000</a>
%e a(84) = 6+28 = 34 since both 6 and 28 divide 84. - _Timothy L. Tiffin_, Jul 14 2016
%t a[n_] := DivisorSum[n, If[DivisorSigma[1, #] == 2#, #, 0]&]; Array[a, 114] (* _Jean-François Alcover_, Dec 18 2015 *)
%o (PARI) a(n)=sumdiv(n,d,(sigma(d,-1)==2)*d) \\ _Charles R Greathouse IV_, Jan 16 2013
%Y Cf. A000396, A185351.
%K nonn
%O 1,6
%A _Timothy L. Tiffin_, Jan 06 2013