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.
%I A331121 #14 Feb 09 2020 02:52:11
%S A331121 2,2,4,2,6,16,4,2,2,6,16,4,4,16,16,2,6,2,4,6,4,16,16,24,2,6,4,4,6,16,
%T A331121 4,2,16,6,16,2,4,24,4,6,6,16,4,16,6,16,16,4,2,2,16,4,6,36,16,36,4,6,
%U A331121 24,16,4,16,4,2,16,16
%N A331121 a(n) is the smallest positive integer k for which tau(k) does not divide sigma(n).
%C A331121 Consecutive t satisfying the equation a(t) = 2 are consecutive elements of A028982 (squares and twice squares).
%C A331121 Conjecture: consecutive u satisfying the equation a(u) = 4 are consecutive elements of a sequence defined as follows: (A024614 \ A088535) \ A074384. The conjecture was checked for 10^6 consecutive integers.
%e A331121 a(10) = 6 because sigma(10) = 18 is divisible by (tau(1) = 1), (tau(2) = 2), (tau(3) = 2), (tau(4) = 3), (tau(5) = 2), and is not divisible by (tau(6) = 4).
%t A331121 Array[Block[{k = 1}, While[Mod[DivisorSigma[1, #], DivisorSigma[0, k]] == 0, k++]; k] &, 66] (* _Michael De Vlieger_, Jan 31 2020 *)
%o A331121 (Maxima) a(n):=(for k:1 while mod(divsum(n), length(divisors(k))) = 0 do z:k, z+1) $ makelist(a(n), n, 1, 100, 1);
%o A331121 (PARI) a(n) = my(k=1, sn=sigma(n)); while ((sn % numdiv(k)) == 0, k++); k; \\ _Michel Marcus_, Jan 10 2020
%Y A331121 Cf. A000005, A000203, A024614, A028982, A074384, A088535.
%K A331121 nonn
%O A331121 1,1
%A A331121 _Lechoslaw Ratajczak_, Jan 10 2020