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

1,2

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.

Links

Table of n, a(n) for n=1..81.

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 *)

Crossrefs

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

Sequence in context: A343721 A070675 A096894 * A070667 A374056 A245349

Adjacent sequences: A097748 A097749 A097750 * A097752 A097753 A097754

Keyword

nonn

Author

Ray Chandler, Aug 26 2004

Status

approved