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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A381743 The number of divisors d of n such that d*n is abundant.

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%I A381743 #10 Mar 06 2025 01:54:44
%S A381743 0,0,0,0,0,3,0,0,0,2,0,6,0,1,0,0,0,6,0,6,0,0,0,8,0,0,0,5,0,8,0,0,0,0,
%T A381743 0,9,0,0,0,8,0,8,0,4,0,0,0,10,0,3,0,4,0,8,0,8,0,0,0,12,0,0,0,0,0,8,0,
%U A381743 2,0,8,0,12,0,0,0,2,0,8,0,10,0,0,0,12,0,0
%N A381743 The number of divisors d of n such that d*n is abundant.
%C A381743 The indices of records of this sequence are the highly composite numbers (A002182) without 2 and 4.
%H A381743 Amiram Eldar, <a href="/A381743/b381743.txt">Table of n, a(n) for n = 1..10000</a>
%F A381743 a(n) = A000005(n) if and only if n is abundant (A005101).
%F A381743 a(n) = A000005(n) - 1 if and only if n is either 1, a perfect number (A000396), or in A341358.
%F A381743 a(n) >= 1 if and only if n is in A381738.
%F A381743 a(n) = 1 if and only if n is in A381742.
%t A381743 a[n_] := DivisorSum[n, 1 &, DivisorSigma[-1, #*n] > 2 &]; Array[a, 100]
%o A381743 (PARI) a(n) = sumdiv(n, d, sigma(d*n, -1) > 2);
%Y A381743 Cf. A000005, A000396, A002182, A005101, A341358, A381738, A381742.
%K A381743 nonn,easy
%O A381743 1,6
%A A381743 _Amiram Eldar_, Mar 06 2025