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A348743 Odd nonsquares k for which A161942(k) >= k, where A161942 is the odd part of sigma.

%I A348743 #29 Aug 21 2025 14:39:06
%S A348743 2205,19845,108045,143325,178605,187425,236925,266805,319725,353925,
%T A348743 372645,407925,452025,462825,584325,637245,646425,658125,672525,
%U A348743 789525,796005,804825,845325,920205,972405,981225,1007325,1055925,1069425,1102725,1113525,1116225,1166445,1201725,1245825,1289925,1378125,1380825,1442925
%N A348743 Odd nonsquares k for which A161942(k) >= k, where A161942 is the odd part of sigma.
%C A348743 The first non-multiples of 5 are a(103) = 6243237 and a(125) = 8164233.
%C A348743 From _Antti Karttunen_, Nov 28 2024: (Start)
%C A348743 This is not a subsequence of A228058. At least k = A000040(28)*(A002110(27)/2)^2 = 15388519572341080054329140040512468358441210638435506649120749687401476705908239675 is a number of the form 4m+3 such that A161942(k) >= k.
%C A348743 Another such number is A000040(28)*81*(A002110(25)/6)^2 = 1279741205456530915782536871495922949062895982530933679752838870798129159675.
%C A348743 Question: What is the smallest term of this sequence that is of the form 4m+3, and thus not in A386427 (in A191218 and in A228058)?
%C A348743 (End)
%H A348743 Antti Karttunen, <a href="/A348743/b348743.txt">Table of n, a(n) for n = 1..55135; terms <= 10^10</a>
%H A348743 <a href="/index/O#opnseqs">Index entries for sequences where odd perfect numbers must occur, if they exist at all</a>
%H A348743 <a href="/index/Se#sequences_which_agree_for_a_long_time">Index entries for sequences which agree for a long time but are different</a>
%H A348743 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%o A348743 (PARI)
%o A348743 A000265(n) = (n >> valuation(n, 2));
%o A348743 isA348743(n) = ((n%2)&&!issquare(n)&&A000265(sigma(n))>=n); \\ Edited Nov 28 2024
%Y A348743 Intersection of A088828 and A348742.
%Y A348743 Cf. A386427 (a subsequence, which agrees for a very long time).
%Y A348743 Cf. A033630, A065205, A083206, A161942, A191218, A228058, A336702, A348741.
%Y A348743 Cf. also A065235, A162284.
%K A348743 nonn,changed
%O A348743 1,1
%A A348743 _Antti Karttunen_, Nov 02 2021
%E A348743 Definition changed (from > to >=) to formally include also any hypothetical odd perfect numbers - _Antti Karttunen_, Nov 28 2024
%E A348743 Comment removed, because it was more related to sequence A386427. - _Antti Karttunen_, Aug 21 2025