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A097751 Least integer with same "mod 4 prime signature" as n. 6
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Jan 10 2013 *)

CROSSREFS

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

Sequence in context: A319704 A070675 A096894 * A070667 A245349 A122416

Adjacent sequences:  A097748 A097749 A097750 * A097752 A097753 A097754

KEYWORD

nonn

AUTHOR

Ray Chandler, Aug 26 2004

STATUS

approved

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Last modified October 14 18:28 EDT 2019. Contains 328022 sequences. (Running on oeis4.)