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A332457 Numbers k such that sigma(k) == 2 modulo 8 and sigma(sigma(k)) == 6 modulo 8.

%I A332457 #18 Nov 23 2024 18:47:01
%S A332457 193,202,673,1153,1201,1354,1601,1642,1873,2017,2088,2593,2682,2753,
%T A332457 3049,3112,3217,3313,3328,3754,3898,4041,4084,4177,4273,4337,4426,
%U A332457 4561,5193,5233,5386,5449,5482,5849,6337,6353,6826,6922,7002,7057,7114,7393,7402,7537,7793,8081,8104,8353,8564,8698,8872,9049,9377,9601
%N A332457 Numbers k such that sigma(k) == 2 modulo 8 and sigma(sigma(k)) == 6 modulo 8.
%C A332457 That the first part of the condition is necessary for odd perfect numbers, see A332228, that the second part of the condition is necessary, see A019283 and A326181.
%H A332457 Antti Karttunen, <a href="/A332457/b332457.txt">Table of n, a(n) for n = 1..10000</a>
%H A332457 <a href="/index/O#opnseqs">Index entries for sequences where any odd perfect numbers must occur</a>
%H A332457 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%t A332457 Select[Range[10000],With[{c=DivisorSigma[1,#]},Mod[c,8]==2&&Mod[DivisorSigma[1,c],8]==6&]]  (* _Harvey P. Dale_, Nov 23 2024 *)
%o A332457 (PARI) isA332457(n) = { my(s=sigma(n)); ((2==(s%8)) && (6==(sigma(s)%8))); };
%o A332457 (Magma) [k:k in [1..9700]| DivisorSigma(1,k) mod 8 eq 2 and DivisorSigma(1, DivisorSigma(1,k)) mod 8 eq 6]; // _Marius A. Burtea_, Feb 15 2020
%Y A332457 Cf. A000203, A019283, A051027, A326181.
%Y A332457 Intersection of A332226 and A332456.
%Y A332457 Cf. A332458 (a subsequence of non-primepower odd terms).
%K A332457 nonn
%O A332457 1,1
%A A332457 _Antti Karttunen_, Feb 15 2020