【摘要】 目的解决数论计数函数均值的计算问题,特别是二进制数字之和和函数七次均值的计算公式问题。方法采用猜想、归纳及推理方法进行了证明。结果得出了二进制数字之和函数七次均值A7(N)的精确计算公式,A7(N)=s-∑1i=0[k7i+1+ki6+1(21+14i)+ki5+1(105+210i+84i2)+ki4+1(35+630i+840i2+280i3)+ki3+1(-210-210i+2 160i2+1 680i3+560i4)+k2i+1(112-420i-840i2+840i3+1 680i4+672i5)+ki+1(224i-560i3+672i5+448i6)+128i7]2ki+1-7。结论此公式对于数论的理论研究和应用具有重要意义。更多还原

【Abstract】 Aim To solve aquestion about number theory counting function mean value,Such as digital function sum of binary system and α(m)-function hypo-mean value.Methods The guess,epagoge,illation are used to solve the guestion.Results The formula of A7(N) is gotten,i.e A7(N)=∑s-1i=0[k7i+1+k6i+1(21+14i)+k5i+1(105+210i+84i2)+k4i+1(35+630i+840i2+280i3)+k3i+1(-210-210i+2 160i2+1 680i3+560i4)+k2i+1(112-420i840i2+840i3+1 680i4+672i5)+ki+1(224i-560i3+672i5+448i6)+128i7]2ki+1-7. Condusion The formula plays a leading role in the studies of number theory and its application.更多还原