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 A348939 #9 Nov 04 2021 20:47:45
%S A348939 45,117,325,333,405,549,605,657,925,1053,1413,1445,1525,1737,1825,
%T A348939 2205,2493,2817,2825,2925,2997,3033,3573,3645,3789,3825,3925,4113,
%U A348939 4825,4869,4941,5445,5517,5733,5913,5949,6057,6425,6525,6597,6813,6925,7025,7497,7605,7825,7893,8125,8325,8425,8973,9225,9477,9837,9925
%N A348939 Odd numbers k for which A064989(sigma(k)) > A064989(k), and which are of the form p^(1+4k) * r^2, where p is prime of the form 1+4m, r > 1, and gcd(p,r) = 1.
%C A348939 Obviously, any hypothetical odd perfect number would be neither in this sequence nor in A348938.
%H A348939 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A348939 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%t A348939 q[n_] := Module[{f = FactorInteger[n]}, p = f[[;; , 1]]; e = f[[;; , 2]]; odde = Select[e, OddQ]; Length[e] > 1 && Length[odde] == 1 && Divisible[odde[[1]] - 1, 4] && Divisible[p[[Position[e, odde[[1]]][[1, 1]]]] - 1, 4]]; f[2, e_] := 1; f[p_, e_] := NextPrime[p, -1]^e; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[1, 10000, 2], q[#] && s[DivisorSigma[1, #]] > s[#] &] (* _Amiram Eldar_, Nov 04 2021 *)
%o A348939 (PARI)
%o A348939 A064989(n) = { my(f = factor(n)); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); factorback(f) };
%o A348939 isA228058(n) = if(!(n%2)||(omega(n)<2),0,my(f=factor(n),y=0); for(i=1,#f~,if(1==(f[i,2]%4), if((1==y)||(1!=(f[i,1]%4)),return(0),y=1), if(f[i,2]%2, return(0)))); (y));
%o A348939 isA348749(n) = ((n%2)&&(A064989(sigma(n)) > A064989(n)));
%o A348939 isA348939(n) = (isA228058(n)&&isA348749(n));
%Y A348939 Intersection of A228058 and A348749.
%Y A348939 Cf. A000203, A064989, A326042, A348938.
%K A348939 nonn
%O A348939 1,1
%A A348939 _Antti Karttunen_, Nov 04 2021