A325819 - OEIS

%I #6 Jun 04 2019 16:33:36

%S 26,84,78,168,118,146,242,182,208,276,200,398,396,322,438,344,390,412,

%T 536,628,432,338,582,472,558,840,512,824,640,726,1022,852,914,628,744,

%U 616,1178,1018,858,1140,856,760,990,936,1490,1014,1564,1482,1104,1096,1196,1138,1008,1550,1556,1180,1474,1158,1508,858,2020

%N a(n) = A324213(A228058(n)).

%C If a(n) > 2 for all n, then there are no odd perfect numbers. See also the conjectures in A324213.

%H Antti Karttunen, <a href="/A325819/b325819.txt">Table of n, a(n) for n = 1..25000</a>

%F a(n) = A324213(A228058(n)).

%o (PARI)

%o up_to = 25000;

%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 A228058list(up_to) = { my(v=vector(up_to), k=0, n=0); while(k<up_to, n++; if(isA228058(n), k++; v[k] = n)); (v); };

%o v228058 = A228058list(up_to);

%o A228058(n) = v228058[n]; \\ _Antti Karttunen_, May 29 2019

%o A324213(n) = { my(s=sigma(n)); sum(i=0, s, (1==gcd(n-i, n-(s-i)))); };

%o A325819(n) = A324213(A228058(n));

%Y Cf. A228058, A324213, A325809.

%K nonn

%O 1,1

%A _Antti Karttunen_, May 29 2019