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A294886
Sum of deficient proper divisors of n.
8
0, 1, 1, 3, 1, 6, 1, 7, 4, 8, 1, 10, 1, 10, 9, 15, 1, 15, 1, 22, 11, 14, 1, 18, 6, 16, 13, 28, 1, 36, 1, 31, 15, 20, 13, 19, 1, 22, 17, 30, 1, 48, 1, 40, 33, 26, 1, 34, 8, 43, 21, 46, 1, 42, 17, 36, 23, 32, 1, 40, 1, 34, 41, 63, 19, 72, 1, 58, 27, 74, 1, 27, 1, 40, 49, 64, 19, 84, 1, 46, 40, 44, 1, 52, 23, 46, 33, 92, 1, 90, 21
OFFSET
1,4
COMMENTS
Sum of divisors of n smaller than n that are deficient numbers (in A005100).
FORMULA
a(n) = Sum_{d|n, d<n} A294934(d)*d.
a(n) = A187793(n) - (A294934(n)*n).
a(n) + A294887(n) = A001065(n).
EXAMPLE
Proper divisors of 90 are: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45. Of these 1, 2, 3, 5, 9, 10, 15 and 45 are in A005100, thus a(90) = 1+2+3+5+9+10+15+45 = 90.
MATHEMATICA
a[n_] := DivisorSum[n, # &, # < n && DivisorSigma[1, #] < 2*# &]; Array[a, 100] (* Amiram Eldar, Mar 14 2024 *)
PROG
(PARI) A294886(n) = sumdiv(n, d, (d<n)*(sigma(d)<(2*d))*d);
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 14 2017
STATUS
approved