素数幂最大公因数序列和的性质

Properties on the Sum of Sequence for the Greatest Common Divisor of Prime Power

给出素数幂的最大公因数序列和S(n)=sum from k=1 to n () d(k),Sα(n)=sum from k=1 to n ()dα(k)的具体公式,其中,p为素数,k为正整数,d(k)=gcd(pk+1,ppk-1+1),并证明Sα(n)(n→!)是发散的.

Let p be a prime number, let k be a positive integer, and d（k）=gcd（pk＋1,ppk-1） The particular formula of the sum of sequence of the greatest common divisor of prime power was given to be as S（n）=n∑k=1d（k）,Sa（n）=n∑k=1da（k） and the scatter of Sa（n）（n→∞） was proved.