A325320 Sum of proper divisors of A228058(n) that are not squarefree; a(n) = -A325314(A228058(n)).

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, 9, 25, 9, 729, 9, 49, 289, 25, 9, 121, 9, 9, 9, 361, 49, 25, 49, 121, 9, 9, 9, 2049, 25, 9, 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

Offset: 1

Author

Antti Karttunen, Apr 22 2019

Keywords

• nonn

Comments

All terms are of the form 4k+1, A016813.

If a(n) is never equal to A325319(n), then there are no odd perfect numbers.

Links

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

Crossrefs

Cf. A016813, A162296, A228058, A325313, A325319, A325378, A325379.

Programs

PARI

A162296(n) = sumdiv(n, d, d*(1-issquarefree(d)));
A325314(n) = (n - A162296(n));
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));
k=0; n=0; while(k<100,n++; if(isA228058(n), k++; print1(-A325314(n), ", ")));

Formula

a(n) = -A325314(A228058(n)) = A162296(A228058(n)) - A228058(n).

a(n) = A325319(n) - A325379(n) = A325378(n) - A325319(n).

a(n) < A001065(A228058(n)) for all n.