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A325319 a(n) = -A325313(A228058(n)).

%I A325319 #11 Apr 22 2019 13:50:11
%S A325319 21,61,81,197,141,241,181,201,381,317,261,301,533,525,361,545,441,689,
%T A325319 761,481,501,697,541,561,773,997,681,1001,741,1305,781,1181,1337,1153,
%U A325319 861,1405,901,961,981,1685,1509,1381,1673,1841,1141,1161,1201,2013,1685,1281,2229,1341,1837,1381,1913,1401,2165,1461,2501,2065,1561,2141
%N A325319 a(n) = -A325313(A228058(n)).
%C A325319 All terms are of the form 4k+1, A016813.
%C A325319 If a(n) is never equal to A325320(n), then there are no odd perfect numbers.
%H A325319 Antti Karttunen, <a href="/A325319/b325319.txt">Table of n, a(n) for n = 1..25000</a>
%F A325319 a(n) = -A325313(A228058(n)) = A228058(n) - A048250(A228058(n)).
%F A325319 a(n) = A325320(n) + A325379(n) = A325378(n) - A325320(n).
%o A325319 (PARI)
%o A325319 A048250(n) = factorback(apply(p -> p+1,factor(n)[,1]));
%o A325319 A325313(n) = (A048250(n) - n);
%o A325319 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 A325319 k=0; n=0; while(k<100,n++; if(isA228058(n), k++; print1(-A325313(n), ", ")));
%Y A325319 Cf. A016813, A048250, A228058, A325313, A325320, A325378, A325379.
%K A325319 nonn
%O A325319 1,1
%A A325319 _Antti Karttunen_, Apr 22 2019