cp's OEIS Frontend

A386427 Odd nondeficient numbers of the form p^(1+4k) * r^2, where p is prime of the form 1+4m, r > 1, and gcd(p,r) = 1.

%I A386427 #15 Aug 21 2025 14:39:25
%S A386427 2205,19845,108045,143325,178605,187425,236925,266805,319725,353925,
%T A386427 372645,407925,452025,462825,584325,637245,646425,658125,672525,
%U A386427 789525,796005,804825,845325,920205,972405,981225,1007325,1055925,1069425,1102725,1113525,1116225,1166445,1201725,1245825,1289925,1378125,1380825
%N A386427 Odd nondeficient numbers of the form p^(1+4k) * r^2, where p is prime of the form 1+4m, r > 1, and gcd(p,r) = 1.
%C A386427 Nondeficient numbers (A023196) that satisfy Euler's condition for odd perfect numbers (A228058).
%C A386427 This is not equal to A348743, as that sequence contains also terms like 1279741205456530915782536871495922949062895982530933679752838870798129159675 and 15388519572341080054329140040512468358441210638435506649120749687401476705908239675, that are lacking from this sequence.
%H A386427 Antti Karttunen, <a href="/A386427/b386427.txt">Table of n, a(n) for n = 1..36000</a>
%H A386427 <a href="/index/O#opnseqs">Index entries for sequences where odd perfect numbers must occur, if they exist at all</a>
%H A386427 <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 A386427 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%o A386427 (PARI)
%o A386427 isA228058(n) = if(!(n%2)||(omega(n)<2), 0, my(f=factor(n), y=0); for(i=1, #f~, if(1==(f[i, 2]%4), if((1==y)||(1!=(f[i, 1]%4)), return(0), y=1), if(f[i, 2]%2, return(0)))); (y));
%o A386427 isA386427(n) = ((sigma(n)>=(2*n)) && isA228058(n));
%Y A386427 Intersection of A023196 and A228058.
%Y A386427 Also the intersection of A083207 and A228058, and probably also of A005835 and A228058. - _Antti Karttunen_, Aug 21 2025
%Y A386427 Subsequence of A348743, from which this eventually differs at some very large n.
%Y A386427 Cf. A386426 (conjectured subsequence).
%K A386427 nonn
%O A386427 1,1
%A A386427 _Antti Karttunen_, Aug 18 2025