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A294929 Number of proper divisors of n that are abundant (A005101). 9
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,36
LINKS
FORMULA
a(n) = Sum_{d|n, d<n} A294937(d).
a(n) = A080224(n) - A294937(n).
a(n) + A294928(n) = A032741(n).
EXAMPLE
The proper divisors of 24 are 1, 2, 3, 4, 6, 8, 12. Only one of these, 12, is abundant (in A005101), thus a(24) = 1.
The proper divisors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60. Six of these are abundant: 12, 20, 24, 30, 40, 60, thus a(120) = 6.
MATHEMATICA
a[n_] := Count[Most[Divisors[n]], _?(DivisorSigma[1, #] > 2*# &)]; Array[a, 100] (* Amiram Eldar, Mar 14 2024 *)
PROG
(PARI) A294929(n) = sumdiv(n, d, (d<n)*(sigma(d)>(2*d)));
CROSSREFS
Cf. also A294902.
Sequence in context: A062977 A357879 A072325 * A076948 A255309 A335446
KEYWORD
nonn
AUTHOR
Antti Karttunen, Nov 14 2017
STATUS
approved

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Last modified March 28 22:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)