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 A380866 #8 Mar 12 2025 08:18:45 %S A380866 18,196,100,36,15376,162,1352,72,968,200,392,13456,144,8450,1032256, %T A380866 400,119072,324,8464,288,1936,5776,2704,4624,111392,450,800,1458,9604, %U A380866 2450,1568,882,2500,576,648,89888,3872,5408,1600,70688,2178,9248,11552,11025,59168,53792,3136,16928,1152,900,43808,26912,3042,30752 %N A380866 a(n) is the least m > 0 such that sigma(m) - 2m = A140863(n). %C A380866 A140863 lists odd numbers k > 0 for which there is a solution to sigma(x) = 2x + k; this sequence lists the smallest such solution. %C A380866 a(44) = 11025 = 105^2 is the first odd term of this sequence. %F A380866 a(n) = (A000203(a(n)) - A140863(n))/2. %e A380866 The smallest (positive) odd number that can occur as abundance A033880 of some abundant number (A005101) is A140863(1) = A033880(18) = 3. Since n = 18 is the least index where 3 appears in A033880, a(1) = 18. %o A380866 (PARI) A380866(n, k=A140863[n])=for(m=1,oo,sigma(m)-2*m==k && return(m)) \\ If the k-value is given as 2nd argument, the first argument is ignored. Otherwise, the vector or list A140863 must be defined up to the n-th element. %Y A380866 Cf. A000203 (sigma), A033880 (abundance: sigma(n)-2n). %Y A380866 Cf. A140863 (odd numbers k = A033880(m) for some m). %K A380866 nonn %O A380866 1,1 %A A380866 _M. F. Hasler_, Mar 10 2025