A374845 - OEIS

%I #8 Aug 03 2024 19:25:57

%S 3,6,7,11,14,19,22,23,31,38,43,46,47,59,62,67,71,79,83,86,94,103,107,

%T 118,127,131,134,139,142,151,158,163,166,167,179,191,199,206,211,214,

%U 223,227,239,251,254,262,263,271,278,283,302,307,311,326,331,334,347,358,359,367,379,382,383,398

%N The numbers p or 2p with p prime and p = 3 mod 4, in ascending order.

%C Numbers appearing exactly once in a Pythagorean triple and as the smallest number in this triple.

%C Subsequence of A292762.

%C Inserting 4 as second term gives A374846.

%H A. Tripathi, <a href="http://www.fq.math.ca/Papers1/46_47-4/Tripathi.pdf">On Pythagorean triples containing a fixed integer</a>, Fib. Q., 46/47 (2008/2009), 331-340. See Theorem 8.

%t t={}; Do[If[(PrimeQ[n]&&Mod[n, 4] == 3)||(PrimeQ[n/2]&&Mod[n/2, 4] == 3), t=Join[t,{n}]], {n, 470}]; t

%t (* Positions of the ones in  A046081, omitting position = 4;  based on program by Jean-François Alcover *)

%t a[1] = 0; a[n_] := Module[{f}, f = Select[FactorInteger[n], Mod[#[[1]], 4] == 1 &][[All, 2]]; (DivisorSigma[0, If[OddQ[n], n, n/2]^2] - 1)/2 + (Times @@ (2*f + 1) - 1)/2]; arr = Array[a, nmax]; fl = Flatten[Position[arr, 1]]; Delete[fl, 2]

%Y Cf. A374846, A292762, A046081.

%K nonn

%O 1,1

%A _Manfred Boergens_, Jul 22 2024