A329607 - OEIS

%I #12 Nov 18 2019 22:03:59

%S 1,2,2,3,2,6,2,5,3,6,2,10,2,6,6,7,2,15,2,10,6,6,2,14,3,6,5,10,2,30,2,

%T 11,6,6,6,21,2,6,6,14,2,30,2,10,10,6,2,22,3,15,6,10,2,35,6,14,6,6,2,

%U 42,2,6,10,13,6,30,2,10,6,30,2,33,2,6,15,10,6,30,2,22,7,6,2,42,6,6,6,14,2,70,6,10,6,6,6,26,2,15,10,21,2,30,2,14,30

%N a(n) = A007947(A122111(n)).

%H Antti Karttunen, <a href="/A329607/b329607.txt">Table of n, a(n) for n = 1..65537</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%F a(n) = A007947(A122111(n)) = A007947(A181819(A108951(n))).

%F a(n) = A122111(A071364(n)).

%F A181821(a(n)) = A329600(n).

%t Block[{f}, f[1] = 1; f[n_] := Module[{l = #, m = 0}, Times @@ Power @@@ Table[l -= m; l = DeleteCases[l, 0]; {Prime@ Length@ l, m = Min@ l}, Length@ Union@ l]] &@ Catenate[ConstantArray[PrimePi[#1], #2] & @@@ FactorInteger@ n]; Array[If[# < 1, 0, Sum[EulerPhi[d] Abs@ MoebiusMu[d], {d, Divisors[#]}]] &@ f[#] &, 105]] (* _Michael De Vlieger_, Nov 18 2019, after _JungHwan Min_ at A122111. *)

%o (PARI)

%o A007947(n) = factorback(factorint(n)[, 1]);

%o A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};

%o A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));

%o A329607(n) = A007947(A122111(n));

%Y Cf. A007947, A064989, A071364, A077462, A108951, A122111, A181819, A181821, A329600.

%K nonn

%O 1,2

%A _Antti Karttunen_, Nov 17 2019