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%I #31 Jan 05 2024 07:04:38
%S 0,4,10,20,41,65,114,185,297,487,809,1339,2253,3824,6544,11297,19620,
%T 34216,59926,105258,185356,327039,577906,1022466,1810789,3209398,
%U 5691825,10099475,17927609,31833805,56541947,100449345,178484340,317187186,563744378,1002052726
%N The difference between A089580(n) and A089579(n).
%C Submitted on the request of _Omar E. Pol_ 17 July 2016. (A089579).
%C a(n) is the sum of A175066(m)-1 over such m that A117453(m)<10^n. - _Andrey Zabolotskiy_, Aug 17 2016
%H Robert G. Wilson v, <a href="/A275358/b275358.txt">Table of n, a(n) for n = 1..100</a>
%F a(n) = A089580(n) - A089579(n).
%F Limit_{n->oo} a(n+1)/a(n) = 1.778279... (A011007). - _Altug Alkan_, Aug 22 2016
%e a(2) = A089580(2)-A089579(2) = 4 because of the three terms: 16 = 2^4 = 4^2, 64 = 2^6 = 4^3 = 8^2 and 81 = 3^4 = 9^2; one for 16, two for 64 and one for 81 making a total of 4.
%t f[n_] := Block[{lim = 10^n -1}, Sum[ (Floor[ lim^(1/k)] - 1)(1 + MoebiusMu[k]), {k, 2, Floor[ Log[2, lim]]}]]; Array[f, 36]
%Y Cf. A011007, A011557, A070428, A089579, A089580.
%K nonn
%O 1,2
%A _Robert G. Wilson v_, Jul 24 2016