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A294889
Sum of abundant proper divisors of n.
8
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 62, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 90, 0, 0, 0, 0, 0, 0, 0, 60, 0, 0, 0, 54, 0, 0, 0, 0, 0, 48, 0, 0, 0, 0, 0, 84, 0, 0, 0, 20, 0, 0, 0, 0, 0
OFFSET
1,24
COMMENTS
Sum of divisors of n smaller than n that are abundant numbers (in A005101).
FORMULA
a(n) = Sum_{d|n, d<n} A294937(d)*d.
a(n) = A187795(n) - (A294937(n)*n).
a(n) + A294888(n) = A001065(n).
EXAMPLE
The proper divisors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30. Of these 12, 20 and 30 are in A005101, thus a(60) = 12+20+30 = 62.
MATHEMATICA
a[n_] := DivisorSum[n, # &, # < n && DivisorSigma[1, #] > 2*# &]; Array[a, 100] (* Amiram Eldar, Mar 14 2024 *)
PROG
(PARI) A294889(n) = sumdiv(n, d, (d<n)*(sigma(d)>(2*d))*d);
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 14 2017
STATUS
approved