A136361 -id:A136361 - cp's OEIS frontend

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

Alexander Adamchuk, Dec 25 2007

nonn

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

			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.

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

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

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

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

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

A136360 Square roots of the perfect squares in A133459.

Original entry on oeis.org

6, 9, 12, 17, 22, 24, 25, 26, 60, 86, 99, 120, 188, 200, 202, 210, 214, 238, 243, 268, 336, 348, 415, 476, 481, 504, 524, 539, 565, 602, 693, 704, 720, 726, 732, 846, 899, 961, 965, 990, 1026, 1202, 1218, 1221, 1224, 1320, 1551, 1602, 1687, 1716, 1724, 1734

Offset: 1

Alexander Adamchuk, Dec 25 2007

nonn

Corresponding squares in A133459 are listed in A136359(n) = a(n)^2.

Note that some numbers in a(n) are also perfect squares: m = k^2 = {9, 25, 961, 17424, ...}. The corresponding numbers k such that a(n) = k^2 are listed in A136361.

			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) = sqrt(36) = 6, a(2) = sqrt(81) = 9, a(3) = sqrt(144) = 12, a(4) = sqrt(289) = 17 that are the square roots of the perfect squares in A133459.

Cf. A136359, A136361, A133459, A002311, A002411, A053721.

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

a(n) = sqrt(A136359(n)).

cp's OEIS Frontend

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

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