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A277449 Numbers n such that there is exactly one nontrivial square n-gonal number. 2
34, 74, 100, 130, 202, 244, 290, 394, 452, 514, 650, 724, 802, 970, 1060, 1154, 1354, 1460, 1570, 1802, 1924, 2050, 2314, 2452, 2594, 2890, 3044, 3202, 3364, 3530, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

LINKS

Muniru A Asiru, Table of n, a(n) for n = 1..238

EXAMPLE

For n = 34, the square 34-gonal numbers are 0, 1, 196.

For n = 74, the square 74-gonal numbers are 0, 1, 2601.

For n = 100, the square 100-gonal numbers are 0, 1, 100.

PROG

(GAP)

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);

F:=List(G, g->[g, DivisorsInt((g-4)^2)]);;

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])] ) );;

N1:=Filtered(List(List([1..Length(N)], k->Filtered(N[k], l->IsPosInt(l[2]))), Set), o->Length(o)>=2);

N2:=Set(Flat(List([1..Length(N1)], i->List([1..Length(N1[i])], j->N1[i][j][1]))));

CROSSREFS

Cf. A005893, A188896, A271624.

Sequence in context: A079863 A154095 A184066 * A063533 A216432 A118619

Adjacent sequences:  A277446 A277447 A277448 * A277450 A277451 A277452

KEYWORD

nonn

AUTHOR

Muniru A Asiru, Oct 16 2016

STATUS

approved

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Last modified May 28 04:51 EDT 2020. Contains 334671 sequences. (Running on oeis4.)