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A332792 a(1) = 1; a(n) = Sum_{d|n, d < n} phi(d) * a(d).

%I A332792 #9 Jan 22 2025 14:28:59
%S A332792 1,1,1,2,1,4,1,6,3,6,1,16,1,8,7,30,1,30,1,34,9,12,1,104,5,14,21,60,1,
%T A332792 96,1,270,13,18,11,278,1,20,15,330,1,174,1,136,81,24,1,1176,7,130,19,
%U A332792 186,1,588,15,804,21,30,1,1204,1,32,135,4590,17,402,1,310,25,348
%N A332792 a(1) = 1; a(n) = Sum_{d|n, d < n} phi(d) * a(d).
%H A332792 Antti Karttunen, <a href="/A332792/b332792.txt">Table of n, a(n) for n = 1..20000</a>
%F A332792 a(1) = 1; a(n) = Sum_{k=1..n, gcd(n, k) > 1} a(n/gcd(n, k)).
%t A332792 a[1] = 1; a[n_] := Sum[If[d < n, EulerPhi[d] a[d], 0], {d, Divisors[n]}]; Table[a[n], {n, 1, 70}]
%t A332792 a[1] = 1; a[n_] := a[n] = Sum[If[GCD[n, k] > 1, a[n/GCD[n, k]], 0], {k, 1, n}]; Table[a[n], {n, 1, 70}]
%o A332792 (PARI)
%o A332792 up_to = 20000;
%o A332792 A332792list(n) = { my(v=vector(n)); v[1] = 1; for(n=2, #v, v[n] = sumdiv(n, d, if(d==n, 0, v[d]*eulerphi(d)))); (v); };
%o A332792 v332792 = A332792list(up_to);
%o A332792 A332792(n) = v332792[n]; \\ _Antti Karttunen_, Jan 22 2025
%Y A332792 Cf. A000010, A006874, A008578 (positions of 1's), A038045, A057660, A332791.
%K A332792 nonn
%O A332792 1,4
%A A332792 _Ilya Gutkovskiy_, Feb 24 2020