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A331597 a(n) = A007947(A331595(n)). 4

%I

%S 1,2,2,3,2,3,2,5,3,3,2,5,2,3,6,7,2,15,2,5,6,3,2,7,3,3,5,5,2,15,2,11,6,

%T 3,6,7,2,3,6,7,2,15,2,5,10,3,2,11,3,15,6,5,2,7,6,7,6,3,2,7,2,3,10,13,

%U 6,15,2,5,6,15,2,11,2,3,15,5,6,15,2,11,7,3,2,7,6,3,6,7,2,7,6,5,6,3,6,13,2,15,10,7,2,15,2,7,30

%N a(n) = A007947(A331595(n)).

%H Antti Karttunen, <a href="/A331597/b331597.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(A331595(n)) = A007947(gcd(A122111(n), A241909(n))).

%t Array[Times @@ FactorInteger[#][[All, 1]] &@ If[# == 1, 1, GCD @@ {Block[{k = #, m = 0}, Times @@ Power @@@ Table[k -= m; k = DeleteCases[k, 0]; {Prime@ Length@ k, m = Min@ k}, Length@ Union@ k]] &@ Catenate[ConstantArray[PrimePi[#1], #2] & @@@ #], Function[t, Times @@ Prime@ Accumulate[If[Length@ t < 2, {0}, Join[{1}, ConstantArray[0, Length@ t - 2], {-1}]] + ReplacePart[t, Map[#1 -> #2 & @@ # &, #]]]]@ ConstantArray[0, Transpose[#][[1, -1]]] &[# /. {p_, e_} /; p > 0 :> {PrimePi@ p, e}]} &@ FactorInteger[#]] &, 105] (* _Michael De Vlieger_, Jan 24 2020, after _JungHwan Min_ at A122111 *)

%o (PARI) A331597(n) = factorback(factorint(gcd(A122111(n), A241909(n)))[, 1]);

%Y Cf. A007947, A064989, A122111, A241909, A331595, A331596.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jan 22 2020

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Last modified June 12 08:13 EDT 2021. Contains 344943 sequences. (Running on oeis4.)