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A294928 Number of proper divisors of n that are nonabundant (A263837).

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%I A294928 #13 Mar 14 2024 03:47:02
%S A294928 0,1,1,2,1,3,1,3,2,3,1,5,1,3,3,4,1,5,1,5,3,3,1,6,2,3,3,5,1,7,1,5,3,3,
%T A294928 3,6,1,3,3,6,1,7,1,5,5,3,1,7,2,5,3,5,1,6,3,7,3,3,1,8,1,3,5,6,3,7,1,5,
%U A294928 3,7,1,7,1,3,5,5,3,7,1,7,4,3,1,9,3,3,3,7,1,9,3,5,3,3,3,8,1,5,5,7,1,7,1,7,7
%N A294928 Number of proper divisors of n that are nonabundant (A263837).
%H A294928 Antti Karttunen, <a href="/A294928/b294928.txt">Table of n, a(n) for n = 1..20000</a>
%F A294928 a(n) = Sum_{d|n, d<n} A294935(d).
%F A294928 a(n) + A294929(n) = A032741(n).
%e A294928 The seven proper divisors of 24 are 1, 2, 3, 4, 6, 8, 12. All except 12 are nonabundant (in A263837), thus a(24) = 6.
%t A294928 a[n_] := DivisorSum[n, 1 &, # < n && DivisorSigma[1, #] <= 2*# &]; Array[a, 100] (* _Amiram Eldar_, Mar 14 2024 *)
%o A294928 (PARI) A294928(n) = sumdiv(n, d, (d<n)*(sigma(d)<=(2*d)));
%Y A294928 Cf. A263837, A294888, A294926, A294927, A294929, A294935.
%Y A294928 Differs from A032741 for the first time at n=24.
%Y A294928 Cf. also A294901.
%K A294928 nonn
%O A294928 1,4
%A A294928 _Antti Karttunen_, Nov 14 2017