A329607 a(n) = A007947(A122111(n)).

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, 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, 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

Offset: 1

Author

Antti Karttunen, Nov 17 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from indices in prime factorization

Crossrefs

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

Programs

Mathematica

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. *)

PARI

A007947(n) = factorback(factorint(n)[, 1]);
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)};
A122111(n) = if(1==n,n,prime(bigomega(n))*A122111(A064989(n)));
A329607(n) = A007947(A122111(n));

Formula

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

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

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