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%I #13 Mar 14 2024 03:48:12
%S 0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,0,0,0,
%T 0,2,0,0,0,1,0,1,0,0,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,3,0,0,0,0,0,1,0,0,
%U 0,1,0,2,0,0,0,0,0,1,0,1,0,0,0,2,0,0,0,1,0,2,0,0,0,0,0,1,0,0,0,1,0,1,0,1,0,0,0,2,0,0,0,1,0,1,0,0,0,0,0,3
%N Number of divisors of n that are primitively abundant (A091191).
%C Records occur at 1, 12, 36, 60, 180, 420, 840, 2520, 7560, 9240, 24024, 60060, ... and they are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, ... Ten occurs for the first time as a(40040) = 10.
%H Antti Karttunen, <a href="/A294890/b294890.txt">Table of n, a(n) for n = 1..70560</a>
%F a(n) = Sum_{d|n} A294930(d).
%e Divisors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. Only 12 is in A091191, thus a(24) = 1.
%e Divisors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. Of these 12 and 18 are found in A091191, thus a(36) = 2.
%t q[n_] := Count[Divisors[n], _?(DivisorSigma[1, #] > 2*# &)] == 1; a[n_] := DivisorSum[n, 1 &, q[#] &]; Array[a, 100] (* _Amiram Eldar_, Mar 14 2024 *)
%o (PARI)
%o A294937(n) = (sigma(n)>(2*n));
%o A294929(n) = sumdiv(n, d, (d<n)*A294937(d));
%o A294930(n) = (A294937(n)*(0==A294929(n)));
%o A294890(n) = sumdiv(n, d, A294930(d));
%Y Cf. A080224, A091191, A294930.
%K nonn
%O 1,36
%A _Antti Karttunen_, Nov 14 2017
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