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 A348935 #15 Nov 04 2021 20:47:27
%S A348935 19,23,31,37,43,47,53,61,67,73,79,83,97,103,107,109,113,127,133,137,
%T A348935 139,149,151,157,163,179,181,191,193,197,199,211,217,223,229,233,239,
%U A348935 241,247,251,257,259,263,269,271,277,281,283,299,301,307,311,313,317,331,335,337,341,347,349,353,359,367,371,373,379
%N A348935 Numbers k congruent to 1 or 5 mod 6, for which A064989(A064989(sigma(k^2))) < A064989(A064989(k^2)), where A064989 shifts the prime factorization one step towards lower primes, and sigma is the sum of divisors function.
%C A348935 Square roots of squares present in A348753.
%C A348935 Any hypothetical odd term y of A005820 must by necessity be a square. If y is also a nonmultiple of 3, then the square root x = A000196(y) of such a number y must satisfy the condition that for all nontrivial unitary divisor pairs d and x/d [with gcd(d,x/d) = 1, 1 < d < x], the other unitary divisor (d) should reside in this sequence, and the other divisor (x/d) in A348936. The explanation is similar to the one given in A348738. See also comments in A348933.
%C A348935 In range 1..2^20, there are 256143 numbers in this sequence and 93381 numbers in A348936.
%C A348935 The composites in this sequence are: 133, 217, 247, 259, 299, 301, 335, 341, 371, etc.
%H A348935 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%H A348935 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%t A348935 f[2, e_] := 1; f[p_, e_] := NextPrime[p, -1]^e; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Range[400], MemberQ[{1, 5}, Mod[#, 6]] && s[s[DivisorSigma[1, #^2]]] < s[s[#^2]] &] (* _Amiram Eldar_, Nov 04 2021 *)
%o A348935 (PARI)
%o A348935 A064989(n) = {my(f); 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 A348935 isA348935(n) = ((n%2)&&(n%3)&&(A064989(A064989(sigma(n^2))) < A064989(A064989(n^2))));
%Y A348935 Cf. A000196, A007310, A348750, A348753, A348933, A348936.
%K A348935 nonn
%O A348935 1,1
%A A348935 _Antti Karttunen_, Nov 04 2021