A325819 a(n) = A324213(A228058(n)).

26, 84, 78, 168, 118, 146, 242, 182, 208, 276, 200, 398, 396, 322, 438, 344, 390, 412, 536, 628, 432, 338, 582, 472, 558, 840, 512, 824, 640, 726, 1022, 852, 914, 628, 744, 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

Offset: 1

Author

Antti Karttunen, May 29 2019

Keywords

• nonn

Comments

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

Links

• Antti Karttunen, Table of n, a(n) for n = 1..25000

Crossrefs

Cf. A228058, A324213, A325809.

Programs

PARI

up_to = 25000;
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));
A228058list(up_to) = { my(v=vector(up_to), k=0, n=0); while(kA228058(n), k++; v[k] = n)); (v); };
v228058 = A228058list(up_to);
A228058(n) = v228058[n]; \\ Antti Karttunen, May 29 2019
A324213(n) = { my(s=sigma(n)); sum(i=0, s, (1==gcd(n-i, n-(s-i)))); };
A325819(n) = A324213(A228058(n));

Formula

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