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

21, 61, 81, 197, 141, 241, 181, 201, 381, 317, 261, 301, 533, 525, 361, 545, 441, 689, 761, 481, 501, 697, 541, 561, 773, 997, 681, 1001, 741, 1305, 781, 1181, 1337, 1153, 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

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 A325320(n), then there are no odd perfect numbers.

Links

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

Crossrefs

Cf. A016813, A048250, A228058, A325313, A325320, A325378, A325379.

Programs

PARI

A048250(n) = factorback(apply(p -> p+1,factor(n)[,1]));
A325313(n) = (A048250(n) - 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(-A325313(n), ", ")));

Formula

a(n) = -A325313(A228058(n)) = A228058(n) - A048250(A228058(n)).

a(n) = A325320(n) + A325379(n) = A325378(n) - A325320(n).