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%I #26 Oct 06 2020 18:46:42
%S 1,1,1,2,4,6,8,22,24,44,112,120,176,520,692,1732,1440,2592,4032,6480,
%T 11088,18720,23760,43200,69984,123120,174960,321732,408240,641520,
%U 1139184,1959552,2799360,5073840,8550684,12830400,20820240,36684900,60993000,101803608,127591200,231575760
%N a(1) = 1, for n > 1: a(n) = phi(sum of the previous terms) where phi is Euler's totient function.
%C a(1) = 1, for n > 1: a(n) = phi(Sum_{i=1..n-1} a(i)) = where phi is A000010. a(n) is the inverse of partial sums of A074693(n), i.e., a(1) = A074693(1), and for n > 1, a(n) = A074693(n) - A074693(n - 1), i.e., the first differences of A074693.
%H David A. Corneth, <a href="/A165931/b165931.txt">Table of n, a(n) for n = 1..450</a>
%e For n = 4, a(4) = phi(a(1) + a(2) + a(3)) = phi(1 + 1 + 1) = phi(3) = 2.
%p b:= proc(n) option remember; `if`(n<2, n,
%p numtheory[phi](b(n-1))+b(n-1))
%p end:
%p a:= n-> b(n)-b(n-1):
%p seq(a(n), n=1..50); # _Alois P. Heinz_, Oct 02 2020
%t a[1] := 1; a[n_] := a[n] = EulerPhi[Plus @@ Table[a[m], {m, n - 1}]]; Table[a[n], {n, 30}]
%o (PARI) first(n) = {my(res = vector(n), t = 1); res[1] = 1; for(i = 2, n, c = eulerphi(t); res[i] = c; t+=c); res} \\ _David A. Corneth_, Oct 02 2020
%Y Cf. A000010, A074693.
%K nonn
%O 1,4
%A _Jaroslav Krizek_, Sep 30 2009
%E Terms verified by _Alonso del Arte_, Oct 12 2009
%E More terms from _David A. Corneth_, Oct 02 2020
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