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 A361683 #48 Mar 22 2023 15:17:55
%S A361683 4,64,4,7168,4,606528,4,64,4,4194304,4
%N A361683 a(n) is the least k such that tau(k) divides sigma_n(k) but not sigma(k), or -1 if no such k exists.
%C A361683 a(13) <= 31525197391593472. - _David A. Corneth_, Mar 20 2023
%C A361683 From _Thomas Scheuerle_, Mar 22 2023: (Start)
%C A361683 a(17) <= 15211807202738752817960438464512 and a(19) <= 2^190*11.
%C A361683 Conjecture: a(n) is of the form 2^b*p1^c*p2^d*...*pk^j with b > 0 and A020639(n) divides b*(c+1)*(d+1)*...*(j+1). (p1, p2, ..., pk are distinct odd prime numbers). (End)
%F A361683 a(2*m) = 4 for m >= 1.
%F A361683 a(6*m-3) = 64 for m >= 1.
%F A361683 From _Thomas Scheuerle_, Mar 22 2023: (Start)
%F A361683 a(m) <= a(A020639(m)) if a(A020639(m)) <> -1.
%F A361683 Conjecture: For primes q > p, a(q) > a(p). If true, we could replace "<=" with "=" in the above formula. (End)
%t A361683 a[n_] := Module[{k = 1, d}, While[Divisible[DivisorSigma[1, k], (d = DivisorSigma[0, k])] || !Divisible[DivisorSigma[n, k], d], k++]; k]; Array[a, 11, 2] (* _Amiram Eldar_, Mar 20 2023 *)
%o A361683 (PARI) isok(k, n) = my(f=factor(k), nd=numdiv(f)); (sigma(f) % nd) && !(sigma(f,n) % nd);
%o A361683 a(n) = my(k=1); while (!isok(k,n), k++); k; \\ _Michel Marcus_, Mar 20 2023
%Y A361683 Cf. A003601, A020486, A046839, A046840.
%Y A361683 Cf. A000005, A000203, A001157, A001158.
%Y A361683 Cf. A020639, A010709 (bisection).
%K A361683 nonn,more
%O A361683 2,1
%A A361683 _Mohammed Yaseen_, Mar 20 2023