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评论
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广义调和数为H(n,m)=和[1/k^m,{k,1,n}]。
对于素数p>3,p^2除以H((p-1)/2,2p),这意味着在{5,7,11,17,23,29,41,53,59,83,89101113131,…}中素数p的a(p)<=p。
注意,许多a(n)的形式为2^m-1(例如,a(1)=7,a(2)=31,a(3)=127,a(6)=8191,等等)。对于n=5+10k,a(n)=5,其中k={1,2,3,4,5,6,7,…}。对于n=1+3k,a(n)=7,其中k={1,2,3,4,5,6,7,9,10,11,12,13,14,15,16,17,19,20,…}。对于n=2+5k,a(n)=31,其中k={2,6,8,9,12,14,…}。
a(50)>3*10^6。
a(51)-a(62)={17,7,53131,5,7,19,7,59,23,7,31}。a(64)-a(77)={7,5,11,7,17,23,7,23,31,7,37,5,7,7}。a(79)-a(119)={7,47263,7,832543,5,43,29,7,89103,7,23,23,7,516193,7,7,11,7101,17,7,13,5,7,31,127,7,37,37,7,113,19,5,29,13,7,7}. a(121)-a(150)={7,31,41,7,5,23,7,37,43,7131,11,7,67,5,7,23,7,4,47,7,111847,5,37,31,7,47127}.
目前,a(n)未知于n={50,63,78120,…}。
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