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%I #8 Aug 19 2024 11:39:10
%S 1,2,3,4,5,6,7,8,9,10,11,11,12,13,14,15,16,16,17,17,18,19,20,20,21,22,
%T 23,23,24,25,26,27,28,29,30,31,32,33,34,34,35,36,37,37,37,38,39,39,40,
%U 40,41,41,42,42,43,43,44,45,46,46,47,48,48,49,50,51,52,52,53,54,55,55
%N Number of powers of squarefree numbers <= n.
%o (Python)
%o from math import isqrt
%o from sympy import mobius, integer_nthroot
%o def A072778(n):
%o def f(x): return int(sum(mobius(k)*(x//k**2) for k in range(1, isqrt(x)+1)))
%o return 2-(m:=n.bit_length())+sum(f(integer_nthroot(n,k)[0]) for k in range(1,m)) # _Chai Wah Wu_, Aug 19 2024
%Y Cf. A072774, A013928.
%K nonn
%O 1,2
%A _Reinhard Zumkeller_, Jul 10 2002