|
%I #12 Jan 24 2020 20:58:38
%S 1,1,1,1,1,3,1,1,2,9,1,5,1,27,1,1,1,1,1,25,3,81,1,7,4,243,2,125,1,5,1,
%T 1,9,729,2,5,1,2187,27,49,1,25,1,625,1,6561,1,11,8,1,81,3125,1,3,1,
%U 343,243,19683,1,35,1,59049,5,1,3,125,1,15625,729,5,1,7,1,177147,2,78125,4,625,1,121,2,531441,1,245,9,1594323,2187,2401,1,21
%N a(n) = A241909(n) / gcd(A122111(n),A241909(n)).
%C It appears that these and the terms of A331598 have the same prime signatures, that is, A046523(a(n)) = A046523(A331598(n)) seems to hold for all n.
%H Antti Karttunen, <a href="/A331599/b331599.txt">Table of n, a(n) for n = 1..10000</a>
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F a(n) = A241909(n) / A331595(n) = A241909(n) / gcd(A122111(n),A241909(n)).
%F a(n) = A331598(A241916(n)).
%t Array[If[# == 1, 1, #2/GCD[#1, #2] & @@ {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[#]] &, 90] (* _Michael De Vlieger_, Jan 24 2020, after _JungHwan Min_ at A122111 *)
%o (PARI) A331599(n) = { my(u=A241909(n)); u/gcd(A122111(n), u); };
%Y Cf. A122111, A241909, A241916, A331595, A331598.
%K nonn
%O 1,6
%A _Antti Karttunen_, Jan 22 2020
|
