A383924 -id:A383924 - cp's OEIS frontend

A383923 Numbers of the form m^p where both p and (m^(p^2) - 1)/(m^p - 1) are prime.

4, 8, 16, 27, 36, 100, 196, 256, 400, 512, 576, 676, 1296, 1331, 1600, 2916, 3136, 4356, 5476, 7056, 8000, 8100, 8836, 9261, 12100, 13456, 14400, 15376, 15876, 16900, 17576, 17956, 21316, 22500, 24336, 25600, 27000, 28900, 30976, 32400, 33856, 41616, 42436, 44100, 50176, 52900

Offset: 1

Max Alekseyev, May 15 2025

nonn

Primes (m^(p^2) - 1)/(m^p - 1) are listed in A383924.
Permutation of A383926.
Cf. A383925.

A383925 Primes of the form (m^(p^2) - 1)/(m^p - 1) with prime p and integer m >= 2.

Original entry on oeis.org

5, 17, 37, 73, 101, 197, 257, 401, 577, 677, 757, 1297, 1601, 2917, 3137, 4357, 5477, 7057, 8101, 8837, 12101, 13457, 14401, 15377, 15877, 16901, 17957, 21317, 22501, 24337, 25601, 28901, 30977, 32401, 33857, 41617, 42437, 44101, 50177, 52901, 55697, 57601, 62501, 65537, 67601, 69697

Offset: 1

Max Alekseyev, May 15 2025

nonn

Corresponding values of m^p are listed in A383926.
Permutation of A383924.
Cf. A383923.

A383926 Powers m^p with prime p, producing primes (m^(p^2) - 1)/(m^p - 1) in A383925.

Original entry on oeis.org

4, 16, 36, 8, 100, 196, 256, 400, 576, 676, 27, 1296, 1600, 2916, 3136, 4356, 5476, 7056, 8100, 8836, 12100, 13456, 14400, 15376, 15876, 16900, 17956, 21316, 22500, 24336, 25600, 28900, 30976, 32400, 33856, 41616, 42436, 44100, 50176, 52900, 55696, 57600, 62500, 65536, 67600, 69696

Offset: 1

Max Alekseyev, May 15 2025

nonn

Permutation of A383923.

Cf. A383924, A383925.

a(n) = m^p with a prime p such that (a(n)^p - 1)/(a(n) - 1) = A383925(n).

cp's OEIS Frontend

A383923 Numbers of the form m^p where both p and (m^(p^2) - 1)/(m^p - 1) are prime.

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A383925 Primes of the form (m^(p^2) - 1)/(m^p - 1) with prime p and integer m >= 2.

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A383926 Powers m^p with prime p, producing primes (m^(p^2) - 1)/(m^p - 1) in A383925.

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