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A187794
Sum of the perfect divisors of n.
7
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, 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, 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
OFFSET
1,6
COMMENTS
Sum of divisors d of n with sigma(d) = 2*d.
Unless an odd perfect number exists, a(n) = 0 whenever n is odd.
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.
The first occurrence of three nonzero values at three consecutive even indices is a(1984) = 496, a(1986) = 6, a(1988) = 28.
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
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
Fixed points: a(n) = n if and only if n is a perfect number (A000396). - Timothy L. Tiffin, Jul 14 2016
LINKS
EXAMPLE
a(84) = 6+28 = 34 since both 6 and 28 divide 84. - Timothy L. Tiffin, Jul 14 2016
MATHEMATICA
a[n_] := DivisorSum[n, If[DivisorSigma[1, #] == 2#, #, 0]&]; Array[a, 114] (* Jean-François Alcover, Dec 18 2015 *)
PROG
(PARI) a(n)=sumdiv(n, d, (sigma(d, -1)==2)*d) \\ Charles R Greathouse IV, Jan 16 2013
CROSSREFS
Sequence in context: A173453 A340979 A102638 * A200214 A294887 A331979
KEYWORD
nonn
AUTHOR
Timothy L. Tiffin, Jan 06 2013
STATUS
approved