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Möbius transform of A003963 (with alternate 0's omitted).
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%I #25 Sep 04 2023 01:59:42

%S 1,1,2,3,2,4,5,2,6,7,3,8,6,4,9,10,4,6,11,5,12,13,4,14,12,6,15,8,7,16,

%T 17,6,10,18,8,19,20,6,12,21,8,22,12,9,23,15,10,14,24,8,25,26,6,27,28,

%U 11,29,16,10,18,20,12,18,30,13,31,21,8,32,33,14,20,18,12,34,35,12,20

%N Möbius transform of A003963 (with alternate 0's omitted).

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>.

%F Multiplicative with a(p^e) = (q-1)q^(e-1) where q = pi(p) = A000720(p). - _David W. Wilson_, Sep 01 2001

%e The Möbius transform begins 1,0,1,0,2,0,3,0,2,0,4,0,5,0,2,0,6,0,7,0,...

%t f[p_, e_] := Module[{q = PrimePi[p]}, (q-1)q^(e-1)]; a[n_] := Times @@ f @@@ FactorInteger[2*n-1]; a[1] = 1; Array[a, 100] (* _Amiram Eldar_, Sep 04 2023 *)

%o (PARI) a(n) = {my(f=factor(2*n-1)); for (i=1, #f~, q = primepi(f[i, 1]); f[i, 1] = (q-1)*q^(f[i,2]-1); f[i, 2] = 1); factorback(f);} \\ _Michel Marcus_, Feb 27 2015

%Y Cf. A000720, A003963.

%K nonn,easy,mult

%O 1,3

%A _Marc LeBrun_

%E More terms from _David W. Wilson_, Aug 29 2001