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 A379949 #35 Mar 12 2025 04:44:37
%S A379949 342225,1029447225,1757705625,2177622225,14787776025,18114198921,
%T A379949 32871503025,45018230625,150897287025,245485566225,296006724225,
%U A379949 705373218225,1126920249225,1329226832241,1358425215225,1545732725625,1555265892609,1783322538921,2811755495241,4627123655625,5248080775161,6140855705625,7683069267225
%N A379949 Primitive abundant numbers (A091191) that are odd squares.
%C A379949 Question: Does A379504(.) obtain generally smaller values for the terms of this subsequence of A156942 than for its non-primitive terms? (See A379951, with A379951(5) = 5969, where A156942(5) = 342225, the first term of this sequence). Is A103977(.) = 1 for all terms, i.e., is this a subsequence of A379503?
%H A379949 Amiram Eldar, <a href="/A379949/b379949.txt">Table of n, a(n) for n = 1..3500</a> (terms 1..725 from Antti Karttunen)
%F A379949 a(n) = A379950(n)^2.
%o A379949 (PARI) is_A379949(n) = if(!(n%2) || !issquare(n) || sigma(n)<=2*n, 0, fordiv(n, d, if(d>1 && sigma(n/d, -1)>2, return(0))); (1));
%o A379949 (PARI) is1(k) = {my(f = factor(k)); for(i = 1, #f~, f[i, 2] *= 2); if(sigma(f, -1) <= 2, return(0)); for(i = 1, #f~, f[i, 2] -= 1; if(sigma(f, -1) > 2, return(0)); f[i, 2] += 1); 1;}
%o A379949 list(lim) = forstep(k = 1, lim, 2, if(is1(k), print1(k^2, ", "))); \\ _Amiram Eldar_, Mar 12 2025
%Y A379949 Cf. A103977, A379504, A379950 (square roots).
%Y A379949 Intersection of A016754 and A091191.
%Y A379949 Intersection of A006038 and A156942.
%Y A379949 Subsequences of the following sequences: A306796 (odd terms, but only if there are no odd perfect numbers), A363176, A379503 (conjectured).
%K A379949 nonn
%O A379949 1,1
%A A379949 _Antti Karttunen_, Jan 07 2025