A079648 -id:A079648 - cp's OEIS frontend

A214084 Triangle read by rows: n-th row = {m: n^2 <= m <= n^3}.

0, 1, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56

Offset: 0

Reinhard Zumkeller, Jul 07 2012

Reinhard Zumkeller, Rows n = 0..15 of triangle, flattened

Cf. A100104 (row lengths), A214085 (row sums), A000290 (left edge), A000578 (right edge), A079648 (number of primes per row).

a214084 n k = a214084_tabf !! n !! k
a214084_row n = a214084_tabf !! n
a214084_tabf = zipWith enumFromTo a000290_list a000578_list

A380332 a(n) = number of primes between n^2 and n^4.

Original entry on oeis.org

0, 0, 4, 18, 48, 105, 199, 342, 546, 825, 1204, 1685, 2300, 3068, 4008, 5143, 6488, 8091, 9956, 12115, 14605, 17446, 20676, 24322, 28441, 33004, 38114, 43805, 50066, 56951, 64529, 72830, 81853, 91751, 102397, 114004, 126516, 140016, 154559, 170186, 186883, 204880, 224009, 244527, 266283, 289506, 314148, 340292, 368114, 397407

Offset: 0

Clark Kimberling, Jan 26 2025

nonn

p(2) = 4 because there are 4 primes between 4 and 16.

Cf. A000040, A000720, A038107, A079648, A380331.

Table[PrimePi[n^4] - PrimePi[n^2], {n, 0, 60}]

a(n) = primepi(n^4) - primepi(n^2); \\ Michel Marcus, Jan 27 2025

from sympy import primepi
def A380332(n): return -primepi(m:=n**2)+primepi(m**2) # Chai Wah Wu, Jan 27 2025

a(n) = PrimePi(n^4) - PrimePi(n^2).

cp's OEIS Frontend

A214084 Triangle read by rows: n-th row = {m: n^2 <= m <= n^3}.

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A380332 a(n) = number of primes between n^2 and n^4.

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