Integers with all prime factors congruent to one modulo four
= Integers with all prime factors congruent to one modulo four
A <positive integer> in this set has no <prime factor> equal to two or congruent to three modulo four. Its <prime factors> all lie in the <residue class> one modulo four. For example $5\cdot13=65$ belongs, while $3^2=9$ does not, even though $9$ itself is congruent to one modulo four. A <half-dimensional interval sieve> bounds the count in an interval of length $z$ by $O(z/\sqrt{\log z})$.