A097751 Least integer with same "mod 4 prime signature" as n.

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, 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, 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

Offset: 1

Author

Ray Chandler, Aug 26 2004

Keywords

• nonn

Comments

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)].

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.

Crossrefs

Cf. A097752, A097753, A097754, A097755, A097756.

Programs

Mathematica

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 *)