A373213 Numbers k such that k^2 - 1 and k^2 + 1 have 6 divisors each.

168, 1368, 97968, 10374840, 16104168, 44049768, 68674368, 100741368, 281803368, 486775968, 1177381968, 1262878368, 1336852968, 2321986968, 2404627368, 3476635368, 4374102768, 5102102040, 5142754368, 5182128168, 5385651768, 6035269968, 9218496168, 10657878168

Offset

1,1

Comments

Each term is a number of the form k = sqrt(p^2 * q + 1) such that q = p^2 - 2 and k^2 + 1 = r^2 * s, where p, q, r, and s are distinct primes.

Links

Table of n, a(n) for n=1..24.

Formula

{ k : tau(k^2 - 1) = tau(k^2 + 1) = 6}, where tau() is the number of divisors function, A000005.

Example

168 is a term: both 168^2 - 1 = 28223 = 13^2 * 167 and 168^2 + 1 = 28225 = 5^2 * 1129 have 6 divisors.

Crossrefs

Cf. A000005, A002522, A005563, A069062, A108278, A193432, A347191, A373209.

Sequence in context: A070835 A112551 A303622 * A263121 A216107 A235932

Adjacent sequences: A373210 A373211 A373212 * A373214 A373215 A373216

Keyword

nonn

Author

Jon E. Schoenfield, Jun 21 2024

Status

approved