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URL: https://oeis.org/A136359

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A136359
Perfect squares in A133459; or perfect squares that are the sums of two nonzero pentagonal pyramidal numbers.
3
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
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[ # ] ] & ]
KEYWORD
nonn
AUTHOR
Alexander Adamchuk, Dec 25 2007
STATUS
approved