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A332218 Numbers k such that A332221(k) = A156552(sigma(k)) is 2*{an odd square}.

%I A332218 #16 May 25 2020 10:01:03
%S A332218 2,162,441,2704,4225,275194921
%N A332218 Numbers k such that A332221(k) = A156552(sigma(k)) is 2*{an odd square}.
%C A332218 Any even term of A332216 must occur also in this sequence.
%H A332218 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%e A332218   a(n)              -> sigma(a(n))              -> A156552(sigma(a(n)))
%e A332218      2 = 2^1 * 1^2  ->    3 = 3^1               ->      2 = 2^1 * 1^1,
%e A332218    162 = 2^1 * 3^4  ->  363 = 3^1 * 11^2        ->     98 = 2^1 * 7^2,
%e A332218    441 = 3^2 * 7^2  ->  741 = 3^1 * 13^1 * 19^1 ->    578 = 2^1 * 17^2,
%e A332218   2704 = 2^4 * 13^2 -> 5673 = 3^1 * 31^1 * 61^1 -> 526338 = 2^1 * 3^6 * 19^2,
%e A332218   4225 = 5^2 * 13^2 -> 5673 = 3^1 * 31^1 * 61^1 -> 526338 = 2^1 * 3^6 * 19^2,
%e A332218 and
%e A332218 275194921 = 53^2 * 313^2 -> 281384229 = 3^1 * 7^1 * 181^2 * 409^1 -> 9671406556943421676716050 = 2^1 * 5^2 * 7^2 * 62829235873^2.
%t A332218 Select[Range@ 5000, And[IntegerQ[#], OddQ[#]] &@ Sqrt[#/2] &@ Floor@ Total@ Flatten@ MapIndexed[#1 2^(#2 - 1) &, Flatten[Table[2^(PrimePi@ #1 - 1), {#2}] & @@@ FactorInteger@ DivisorSigma[1, #]]] &] (* _Michael De Vlieger_, Feb 12 2020 *)
%o A332218 (PARI)
%o A332218 \\ Needs also code from A156552:
%o A332218 istosq(n) = ((1==valuation(n,2))&&issquare(n/2));
%o A332218 for(n=1,2^25,if(istosq(A156552(sigma(n*n))),print1(n*n,", ")); if(istosq(A156552(sigma(2*n*n))),print1(2*n*n,", ")));
%Y A332218 Cf. A000203, A156552, A332216, A332217, A332221.
%Y A332218 Subsequence of A332217 ⊂ A067051 ⊂ A028982.
%K A332218 nonn,more
%O A332218 1,1
%A A332218 _Antti Karttunen_, Feb 11 2020