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A325319
a(n) = -A325313(A228058(n)).
8
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
1,1
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
FORMULA
a(n) = -A325313(A228058(n)) = A228058(n) - A048250(A228058(n)).
a(n) = A325320(n) + A325379(n) = A325378(n) - A325320(n).
PROG
(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), ", ")));
KEYWORD
nonn
AUTHOR
Antti Karttunen, Apr 22 2019
STATUS
approved