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Odd numbers k for which A161942(k) > k, where A161942 is the odd part of sigma.
5

%I #10 Nov 02 2021 15:59:16

%S 9,25,49,81,121,169,225,289,361,441,529,625,729,841,961,1089,1225,

%T 1369,1521,1681,1849,2025,2205,2209,2401,2601,2809,3025,3249,3481,

%U 3721,3969,4225,4489,4761,5041,5329,5625,5929,6241,6561,6889,7225,7569,7921,8281,8649,9025,9409,9801,10201,10609,11025,11449,11881,12321

%N Odd numbers k for which A161942(k) > k, where A161942 is the odd part of sigma.

%C All odd squares (A016754) are present, but not all terms are squares. A348743 gives the nonsquare terms.

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>

%t odd[n_] := n/2^IntegerExponent[n, 2]; Select[Range[1, 10^4, 2], odd[DivisorSigma[1, #]] > # &] (* _Amiram Eldar_, Nov 02 2021 *)

%o (PARI)

%o A000265(n) = (n >> valuation(n, 2));

%o isA348742(n) = ((n%2)&&A000265(sigma(n))>n);

%Y Union of A016754 and A348743.

%Y Cf. A161942, A348741.

%Y Cf. also A348739.

%K nonn

%O 1,1

%A _Antti Karttunen_, Nov 02 2021