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A137409 Numbers that cannot be the value of 'C' in a primitive Pythagorean triple (A < B; A^2 + B^2 = C^2).

%I A137409 #43 May 08 2021 02:22:55
%S A137409 1,2,3,4,6,7,8,9,10,11,12,14,15,16,18,19,20,21,22,23,24,26,27,28,30,
%T A137409 31,32,33,34,35,36,38,39,40,42,43,44,45,46,47,48,49,50,51,52,54,55,56,
%U A137409 57,58,59,60,62,63,64,66,67,68,69,70,71,72,74,75,76,77,78,79,80,81,82,83
%N A137409 Numbers that cannot be the value of 'C' in a primitive Pythagorean triple (A < B; A^2 + B^2 = C^2).
%C A137409 Complement of A008846. - _R. J. Mathar_, Aug 15 2010
%C A137409 A024362(a(n)) = 0. - _Reinhard Zumkeller_, Dec 02 2012
%C A137409 Except for the 1st term 1, complement of A004613. - _Federico Provvedi_, Jan 26 2019
%C A137409 After 1, numbers k for which A065338(k) > 1, i.e., after 1, numbers all of whose prime divisors are not of the form 4u+1. - _Antti Karttunen_, Dec 26 2020
%H A137409 Reinhard Zumkeller, <a href="/A137409/b137409.txt">Table of n, a(n) for n = 1..10000</a>
%e A137409 3,4,5; number 5 is not in this sequence.
%e A137409 5,12,13; number 13 is not in this sequence.
%e A137409 8,15,17; number 17 is not in this sequence.
%e A137409 7,24,25; number 25 is not in this sequence.
%t A137409 okQ[1] = True;
%t A137409 okQ[n_] := AnyTrue[FactorInteger[n][[All, 1]], Mod[#, 4] != 1&];
%t A137409 Select[Range[100], okQ] (* _Jean-François Alcover_, Mar 10 2019, after _Federico Provvedi_'s comment *)
%o A137409 (Haskell)
%o A137409 import Data.List (elemIndices)
%o A137409 a137409 n = a137409_list !! (n-1)
%o A137409 a137409_list = map (+ 1) $ elemIndices 0 a024362_list
%o A137409 -- _Reinhard Zumkeller_, Dec 02 2012
%o A137409 (PARI)
%o A137409 A065338(n) = { my(f = factor(n)); for (i=1, #f~, f[i, 1] = (f[i, 1]%4)); factorback(f); };
%o A137409 isA137409(n) = ((1==n)||(A065338(n)>1)); \\ _Antti Karttunen_, Dec 26 2020
%Y A137409 Cf. A004613, A008846, A020882, A024362, A065338, A137407.
%Y A137409 Subsequences: A125667 (the odd terms), A339875.
%K A137409 nonn
%O A137409 1,2
%A A137409 _Vladimir Joseph Stephan Orlovsky_, Apr 14 2008
%E A137409 Extended by _R. J. Mathar_, Aug 15 2010