|
%I #11 Jan 15 2013 12:07:05
%S 1,2,3,4,5,6,3,8,9,10,3,12,5,6,15,16,5,18,3,20,21,6,3,24,25,10,27,12,
%T 5,30,3,32,21,10,15,36,5,6,15,40,5,42,3,12,45,6,3,48,9,50,15,20,5,54,
%U 15,24,21,10,3,60,5,6,63,64,65,42,3,20,21,30,3,72,5,10,75,12,21,30,3,80,81
%N Least integer with same "mod 4 prime signature" as n.
%C For n=2^a_0*p_1^a_1*...*p_n^a_n*q_1^b_1*...*q_m^b_m where p_i is a prime of form 4k+3, q_i is a prime of the form 4k+1, with a_1>=a_2>=...>=a_n and b_1>=b_2>=...>=b_m, define "mod 4 prime signature" to be ordered prime exponents [a_0,(a_1,...,a_n),(b_1,...,b_m)].
%C Least integer with a given "mod 4 prime signature" is obtained by replacing p_i with i-th prime of form 4k+3 and q_i with i-th prime of form 4k+1.
%t mod4PrimeSignature[n_] := {fi = FactorInteger[n]; If[OddQ[n], 0, fi[[1, 2]]], Select[fi, Mod[#[[1]], 4] == 3 &][[All, 2]]//Sort, Select[fi, Mod[#[[1]], 4] == 1 &][[All, 2]]}; a[n_] := Catch[ For[k = 2, True, k++, If[ mod4PrimeSignature[k] == mod4PrimeSignature[n], Throw[k]]]]; a[1] = 1; Table[a[n], {n, 1, 81}] (* _Jean-François Alcover_, Jan 10 2013 *)
%Y Cf. A097752, A097753, A097754, A097755, A097756.
%K nonn
%O 1,2
%A _Ray Chandler_, Aug 26 2004
|
