A319309
Expansion of theta_4(q)^24 in powers of q = exp(Pi i t).
Original entry on oeis.org
1, -48, 1104, -16192, 170064, -1362336, 8662720, -44981376, 195082320, -721175536, 2319457632, -6631997376, 17231109824, -41469483552, 93703589760, -200343312768, 407488018512, -793229226336, 1487286966928, -2697825744960, 4744779429216, -8110465650176
Offset: 0
A127308
Number of ways of writing the n-th prime prime(n) as a sum of 24 squares.
Original entry on oeis.org
1104, 16192, 1362336, 44981376, 6631997376, 41469483552, 793229226336, 2697825744960, 22063059606912, 282507110257440, 588326886375936, 4119646755044256, 12742799887509216, 21517654506205632, 57242599902057216
Offset: 1
For prime(1) = 2, two of the 24 squares are (+-1)^2 and the other 22 are 0^2, so a(1) = 2*2*binomial(24,2) = 4*276 = 1104.
- E. Grosswald, Representations of Integers as Sums of Squares, Springer-Verlag, NY, 1985, p. 107.
- Barry Mazur, Controlling our errors, Nature 443, 7 (2006) 38-40.
- N. J. A. Sloane, Table of n, a(n) for n = 1..70
- Barry Mazur, The Structure of Error Terms in Number Theory and an Introduction to the Sato-Tate Conjecture, Current Events Bulletin, Amer. Math. Soc., 2007.
- Barry Mazur, Controlling our errors
- Barry Mazur, Finding meaning in error terms, Bull. Amer. Math. Soc., 45 (No. 2, 2008), 185-228.
- Tony Phillips, Math in the Media
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Table[SquaresR[24, Prime[n]], {n, 1, 70}]
Table[Abs[16/691 (p^11 + 1) + 33152/691 RamanujanTau[p]], {p, Prime@Range@70}] (* Giorgos Kalogeropoulos, Dec 15 2022 *)
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