A136359 -id:A136359 - cp's OEIS frontend

A136360 Square roots of the perfect squares in A133459.

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)).

A136361 Square roots of the perfect squares in A136360; or numbers k such that k^4 is in A133459 = the sums of two nonzero pentagonal pyramidal numbers.

Original entry on oeis.org

3, 5, 31, 132, 1068, 9672, 50664, 145060

Offset: 1

Alexander Adamchuk, Dec 25 2007

Corresponding perfect squares in A136360 are a(n)^2 = {9, 25, 961, 17424, ...}. They correspond to the perfect fourth powers in A133459 = Sums of two nonzero pentagonal pyramidal numbers. a(n)^4 are the terms of A133459: {81, 525, 923521, 303595776, ...}. Note that the first three terms are prime.

a(9) > (5*10^20)^(1/4). - Donovan Johnson, Jun 12 2011

Cf. A136359, A136360, A133459, A002311, A002411, A053721.

Name corrected and a(5)-a(6) from Donovan Johnson, Nov 20 2010

a(7)-a(8) from Donovan Johnson, Jun 12 2011

cp's OEIS Frontend

A136360 Square roots of the perfect squares in A133459.

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