OFFSET
1,1
COMMENTS
Corresponding values of tau(a(n)-1): 3, 5, 17, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, ...
Corresponding values of tau(a(n)-2) = tau(a(n)-3): 2, 4, 16, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, ...
Quadruples of [tau(a(n)-3), tau(a(n)-2), tau(a(n)-1), tau(a(n))]: [2, 2, 3, 2], [4, 4, 5, 2], [16, 16, 17, 2], [32, 32, 33, 2], [32, 32, 33, 2], [32, 32, 33, 2], [32, 32, 33, 2], [32, 32, 33, 2], [32, 32, 33, 2], ...
Quadruple [32, 32, 33, 2] holds for all 128 terms 65537 < a(n) < 10^15.
Number p-1 is a perfect square as its number of divisors is odd.
The first 3 terms are Fermat primes from A019434.
Term 103565955613697 is the smallest primes p such that tau(p - 1) - 1 = tau(p - 2) = tau(p - 3) = tau(p - 4).
EXAMPLE
Quadruple of [tau(65534), tau(65535), tau(65536), tau(65537)]: [16, 16, 17, 2].
PROG
(Magma) [m: m in [4..10^6] | IsPrime(m) and #Divisors(m - 1) eq #Divisors(m - 2) + 1 and #Divisors(m - 2) eq #Divisors(m - 3)]
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Mar 03 2022
STATUS
approved