cp's OEIS Frontend

A277449 Numbers n such that there is exactly one nontrivial square n-gonal number.

%I A277449 #33 Dec 01 2017 01:22:42
%S A277449 34,74,100,130,202,244,290,394,452,514,650,724,802,970,1060,1154,1354,
%T A277449 1460,1570,1802,1924,2050,2314,2452,2594,2890,3044,3202,3364,3530,
%U A277449 3700,3874,4234,4420,4610,5002,5204,5410,5834,6052,6274,6730,6964,7202,7690,7940,8194,8714,8980,9250,9802,10084,10370,10954,11252,11554,12170,12484,12802,13450,13780
%N A277449 Numbers n such that there is exactly one nontrivial square n-gonal number.
%C A277449 There are infinitely many squares that are triangular, pentagonal, hexagonal, etc. Also there is no square 10-gonal number, 20-gonal number, 52-gonal number, 64-gonal number, etc. greater than 1 (see A188896). Other than the trivial square n-gonal numbers 0 and 1, there is exactly one square 34-gonal number, one square 74-gonal number, one square 100-gonal number, one square 130-gonal number, etc.
%H A277449 Muniru A Asiru, <a href="/A277449/b277449.txt">Table of n, a(n) for n = 1..238</a>
%e A277449 For n = 34, the square 34-gonal numbers are 0, 1, 196.
%e A277449 For n = 74, the square 74-gonal numbers are 0, 1, 2601.
%e A277449 For n = 100, the square 100-gonal numbers are 0, 1, 100.
%o A277449 (GAP)
%o A277449 G:=[];; for g in [5..100000]  do for r in [1..5000] do if 2*g-4=r^2 then Add(G,g); fi; od; od; G; Length(G);
%o A277449 F:=List(G,g->[g,DivisorsInt((g-4)^2)]);;
%o A277449 N:=List([1..Length(F)], i->List([1..Length(F[i][2])],j->[F[i][1],((F[i][1]-4)*(F[i][1]-4+2*F[i][2][j])+F[i][2][j]^2)/((4*F[i][1]-8)*F[i][2][j])] ) );;
%o A277449 N1:=Filtered(List(List([1..Length(N)],k->Filtered(N[k], l->IsPosInt(l[2]))),Set),o->Length(o)>=2);
%o A277449 N2:=Set(Flat(List([1..Length(N1)],i->List([1..Length(N1[i])],j->N1[i][j][1]))));
%Y A277449 Cf. A005893, A188896, A271624.
%K A277449 nonn
%O A277449 1,1
%A A277449 _Muniru A Asiru_, Oct 16 2016