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%I #29 Jun 15 2021 01:29:29
%S 0,1,2,1,2,6,7,5,0,6,7,6,7,15,22,15,16,12,13,10,19,31,32,30,11,25,10,
%T 5,6,28,29,15,28,46,57,46,47,67,82,76,77,107,108,99,80,104,105,92,51,
%U 33,52,41,42,30,45,35,56,86,87,86,87,119,90,59,76,122,123,108,133,179,180
%N a(n) = Sum_{k=1..n} (core(k) - phi(k)), where core(k) is the squarefree part of k.
%C a(n) is always >= 0.
%H Amiram Eldar, <a href="/A070236/b070236.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SquarefreePart.html">Squarefree Part</a>.
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TotientFunction.html">Totient Function</a>.
%F a(n) = A069891(n) - A002088(n) = Sum_{k=1..n} (A007913(k) - A000010(k)).
%F Asymptotically: a(n) = (Pi^2/30 - 3/Pi^2)*n^2 + O(n*log(n)).
%t f[n_] := Times @@ (First[#]^Mod[Last[#], 2] & /@ FactorInteger[n]) - EulerPhi[n]; Accumulate @ Array[f, 100] (* _Amiram Eldar_, Sep 06 2020 *)
%o (PARI) for(n=1,100,print1(sum(i=1,n,core(i)-eulerphi(i)),","))
%Y Cf. A000010, A002088, A007913, A069891.
%K easy,nonn
%O 1,3
%A _Benoit Cloitre_, May 08 2002
%E Various sections edited by _Petros Hadjicostas_, May 11 2020
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