A136359 Perfect squares in A133459; or perfect squares that are the sums of two nonzero pentagonal pyramidal numbers.

36, 81, 144, 289, 484, 576, 625, 676, 3600, 7396, 9801, 14400, 35344, 40000, 40804, 44100, 45796, 56644, 59049, 71824, 112896, 121104, 172225, 226576, 231361, 254016, 274576, 290521, 319225, 362404, 480249, 495616, 518400, 527076, 535824

Offset

1,1

Comments

Corresponding numbers m such that m^2 = a(n) are listed in A136360.

Note that some numbers in A136360 are also perfect squares. The corresponding numbers k such that m = k^2 are listed in A136361.

Includes all nonzero members of A099764: this occurs when the two pentagonal pyramidal numbers are both equal to i^2*(i+1)/2 where i+1 is a square. - Robert Israel, Feb 04 2020

Links

Robert Israel, Table of n, a(n) for n = 1..985

Formula

a(n) = A136360(n)^2.

Example

A133459 begins {2, 7, 12, 19, 24, 36, 41, 46, 58, 76, 80, 81, 93, 115, 127, 132, 144, 150, 166, 197, 201, 202, 214, 236, 252, 271, 289, ...}.
Thus a(1) = 36, a(2) = 81, a(3) = 144, a(4) = 289 that are the perfect squares in A133459.

Maple

N:= 200: # for terms up to N^2*(N+1)/2.
PP:= [seq(i^2*(i+1)/2, i=1..N)]:
PP2:= sort(convert(select(`<=`, {seq(seq(PP[i]+PP[j], j=i..N), i=1..N)}, PP[-1]), list)):
select(issqr, PP2); # Robert Israel, Feb 04 2020

Mathematica

Select[ Intersection[ Flatten[ Table[ i^2*(i+1)/2 + j^2*(j+1)/2, {i, 1, 300}, {j, 1, i} ] ] ], IntegerQ[ Sqrt[ # ] ] & ]

Crossrefs

Cf. A136360, A136361, A133459, A002311, A002411, A053721, A099764.

Sequence in context: A335276 A271629 A171675 * A257649 A259240 A341555

Adjacent sequences: A136356 A136357 A136358 * A136360 A136361 A136362

Keyword

nonn

Author

Alexander Adamchuk, Dec 25 2007

Status

approved