A097752 Least integer with each "mod 4 prime signature".

1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 21, 24, 25, 27, 30, 32, 36, 40, 42, 45, 48, 50, 54, 60, 63, 64, 65, 72, 75, 80, 81, 84, 90, 96, 100, 105, 108, 120, 125, 126, 128, 130, 135, 144, 150, 160, 162, 168, 180, 189, 192, 195, 200, 210, 216, 225, 231, 240, 243

Offset

1,2

Comments

See A097751 for definition of "mod 4 prime signature".

A097751 sorted and duplicates removed; n such that A097751(n)=n.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Charles R Greathouse IV, PARI/GP script to find terms of this sequence

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]]}; A097751[n_] := Catch[For[k = 2, True, k++, If[ mod4PrimeSignature[k] == mod4PrimeSignature[n], Throw[k]]]]; A097751[1] = 1; Select[ Range[243], A097751[#] == # &] (* Jean-François Alcover, Jan 10 2013 *)

Prog

(PARI) is(n)=n>>=valuation(n, 2); my(e3=valuation(n, 3), e1=valuation(n, 5), e); n/=3^e3 * 5^e1; forprime(p=7, , e=valuation(n, p); if(p%4==1, if(e1<e, return(0)); e1=e, if(e3<e, return(0)); e3=e); if(e, n/=p^e, if(e1==0 && e3==0, return(n==1)))) \\ Charles R Greathouse IV, Dec 10 2016
(PARI) See Greathouse link.

Crossrefs

Cf. A097751, A097753, A097754, A097755, A097756.

Sequence in context: A010432 A187041 A364560 * A014866 A051661 A051037

Adjacent sequences: A097749 A097750 A097751 * A097753 A097754 A097755

Keyword

nonn

Author

Ray Chandler, Aug 26 2004

Status

approved