A294929 - OEIS

%I #13 Mar 14 2024 03:46:26

%S 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,

%T 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,

%U 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

%N Number of proper divisors of n that are abundant (A005101).

%H Antti Karttunen, <a href="/A294929/b294929.txt">Table of n, a(n) for n = 1..20000</a>

%F a(n) = Sum_{d|n, d<n} A294937(d).

%F a(n) = A080224(n) - A294937(n).

%F a(n) + A294928(n) = A032741(n).

%e 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.

%e 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.

%t a[n_] := Count[Most[Divisors[n]], _?(DivisorSigma[1, #] > 2*# &)]; Array[a, 100] (* _Amiram Eldar_, Mar 14 2024 *)

%o (PARI) A294929(n) = sumdiv(n, d, (d<n)*(sigma(d)>(2*d)));

%Y Cf. A005101, A032741, A080224, A294889, A294926, A294927, A294928, A294930, A294937.

%Y Cf. also A294902.

%K nonn

%O 1,36

%A _Antti Karttunen_, Nov 14 2017