%I #8 Sep 19 2021 22:02:39
%S 273,399,651,741,903,1209,1407,1533,1659,1677,1767,2037,2163,2331,
%T 2451,2457,2613,2667,2847,3003,3081,3297,3423,3591,3685,3783,3819,
%U 3843,3885,3999,4017,4095,4161,4179,4329,4345,4389,4431,4503,4683,4953,5061,5187,5529,5691,5817,5859,5871,5985,6123,6231,6279,6327,6357
%N Odd numbers k for which A003415(sigma(k^2))-(k^2) is strictly positive and a multiple of six. Here A003415 is the arithmetic derivative.
%C A square root of any hypothetical odd term x (if such numbers exist) in A005820 (triperfect numbers) should be a member of this sequence. See comments in A347882, A347887 and also in A347870 and in A347391.
%C Of the first 200 terms of A097023, 44 appear also in this sequence, the first ones being 50281, 73535, 379953, etc.
%t ad[1] = 0; ad[n_] := n * Total@(Last[#]/First[#]& /@ FactorInteger[n]); Select[Range[1, 6500, 2], (d = ad[DivisorSigma[1, #^2]] - #^2) > 0 && Divisible[d, 6] &] (* _Amiram Eldar_, Sep 19 2021 *)
%o (PARI)
%o A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o isA347888(n) = if(!(n%2),0,my(u=(A003415(sigma(n^2))-(n^2))); ((u>0)&&!(u%6)));
%Y Intersection of A347882 and A347887. Subsequence of A347881 and of A347885.
%Y Cf. A000203, A003415, A005820, A097023, A235991, A235992, A342923, A342925, A342926, A347383, A347391.
%K nonn
%O 1,1
%A _Antti Karttunen_, Sep 19 2021