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A294887
Sum of nondeficient proper divisors of n.
7
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 36, 0, 0, 0, 20, 0, 6, 0, 0, 0, 0, 0, 42, 0, 0, 0, 0, 0, 24, 0, 28, 0, 0, 0, 68, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 96, 0, 0, 0, 0, 0, 6, 0, 60, 0, 0, 0, 88, 0, 0, 0, 0, 0, 54, 0, 0, 0, 0, 0, 90, 0, 0, 0, 20, 0, 6, 0, 0, 0
OFFSET
1,12
COMMENTS
Sum of divisors n smaller than n that are nondeficient numbers (in A023196).
FORMULA
a(n) = Sum_{d|n, d<n} A294936(d)*d. - Typo in A-number corrected by Antti Karttunen, Apr 04 2022
a(n) + A294886(n) = A001065(n).
EXAMPLE
Proper divisors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, and 45. Of these 6, 18 and 30 are in A023196, thus a(90) = 6+18+30 = 54.
MATHEMATICA
a[n_] := DivisorSum[n, # &, # < n && DivisorSigma[1, #] >= 2*# &]; Array[a, 100] (* Amiram Eldar, Mar 14 2024 *)
PROG
(PARI) A294887(n) = sumdiv(n, d, (d<n)*(sigma(d)>=(2*d))*d);
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 14 2017
STATUS
approved