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%I #25 Sep 14 2023 02:30:46
%S 1,1,2,2,4,2,7,4,6,4,12,4,20,7,8,8,33,6,54,8,14,12,88,8,20,20,18,14,
%T 143,8,232,16,24,33,28,12,376,54,40,16,609,14,986,24,24,88,1596,16,56,
%U 20,66,40,2583,18,48,28,108,143,4180,16,6764,232,42,32,80,24,10945,66
%N Möbius transform of A003965.
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>.
%F Multiplicative with a(p^e) = (q-1)q^(e-1) were q = Fibonacci(pi(p)+2) = A000045(A000720(p)+2). - _David W. Wilson_, Sep 01 2001
%F Sum_{n>=1} 1/a(n) = Product_{k>=3} (1 + Fibonacci(k)/(Fibonacci(k)-1)^2) = 9.955734312016908009501... . - _Amiram Eldar_, Sep 14 2023
%t a[n_] := If[n == 1, 1, Product[{p, e} = pe; q = Fibonacci[PrimePi[p] + 2]; (q-1) q^(e-1), {pe, FactorInteger[n]}]];
%t Array[a, 100] (* _Jean-François Alcover_, Sep 29 2020 *)
%o (PARI) a(n) = {my(f = factor(n), p = f[, 1], e = f[, 2], q); prod(i = 1, #p, q = fibonacci(primepi(p[i])+2); (q-1)*q^(e[i]-1));} \\ _Amiram Eldar_, Sep 14 2023
%Y Cf. A000045, A000720, A003965.
%K nonn,easy,mult
%O 1,3
%A _Marc LeBrun_
%E More terms from _David W. Wilson_, Aug 29 2001
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