|
%I #11 Apr 22 2019 13:50:17
%S 9,9,9,49,9,25,9,9,297,25,9,9,121,49,9,25,9,49,169,9,9,25,9,9,25,585,
%T 9,25,9,729,9,49,289,25,9,121,9,9,9,361,49,25,49,121,9,9,9,2049,25,9,
%U 1161,9,25,9,25,9,49,9,529,25,9,25,9,169,2381,49,1449,9,9,9,1593,9,25,9,121,9,49,9,2889,9,25,289,9,2997,9
%N Sum of proper divisors of A228058(n) that are not squarefree; a(n) = -A325314(A228058(n)).
%C All terms are of the form 4k+1, A016813.
%C If a(n) is never equal to A325319(n), then there are no odd perfect numbers.
%H Antti Karttunen, <a href="/A325320/b325320.txt">Table of n, a(n) for n = 1..25000</a>
%F a(n) = -A325314(A228058(n)) = A162296(A228058(n)) - A228058(n).
%F a(n) = A325319(n) - A325379(n) = A325378(n) - A325319(n).
%F a(n) < A001065(A228058(n)) for all n.
%o (PARI)
%o A162296(n) = sumdiv(n, d, d*(1-issquarefree(d)));
%o A325314(n) = (n - A162296(n));
%o 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 k=0; n=0; while(k<100,n++; if(isA228058(n), k++; print1(-A325314(n), ", ")));
%Y Cf. A016813, A162296, A228058, A325313, A325319, A325378, A325379.
%K nonn
%O 1,1
%A _Antti Karttunen_, Apr 22 2019
|
