Sums of Numbers with Many Divisors Original Research Article

Letkbe a fixed integer,kgreater-or-equal, slanted2, and suppose thatvar epsilon>0. We show that every sufficiently large integerncan be expressed in the formn=m1+m2+…+mkwhered(mi)>n(log 2−var epsilon)(1−1/k)/log log nfor alli. This is best possible, since there are infinitely many exceptionalnif the factor log 2−var epsilonis replaced by log 2+var epsilon.