OFFSET
1,1
COMMENTS
tau(k) is the number of positive divisors of k (A000005).
Lesser of twin primes (A001359) are terms. If p is lesser of twin primes then tau(p^(p+1)) = p + 2 (see A006512).
Sequence of composite terms c: 4, 25, 49, 125, 343, 529, 1369, ...; (tau(c^(c+1)): 11, 53, 101, 379, 1033, 1061, 2741, ...).
Numbers of the form p^k where p is prime and 1 + k * (1 + p^k) is prime. - Robert Israel, Sep 02 2024
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
tau(4^5) = tau(1024) = 11 (prime).
MAPLE
N:= 10000: # for terms <= N
P:= select(isprime, [2, seq(i, i=3..N, 2)]):
R:= {}:
for p in P do
Qs:= select(q -> isprime(1 + q + q*p^q), {$1..ilog[p](N)});
R:= R union map(q -> p^q, Qs)
od:
sort(convert(R, list)); # Robert Israel, Sep 02 2024
MATHEMATICA
Select[Range[1319], PrimeQ@DivisorSigma[0, #^(# + 1)] &] (* Giovanni Resta, Mar 07 2017 *)
PROG
(Magma) [n: n in [1..500] | IsPrime(NumberOfDivisors(n^(n+1)))];
(PARI) isok(n) = isprime(numdiv(n^(n+1))); \\ Michel Marcus, Mar 07 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Jaroslav Krizek, Mar 07 2017
STATUS
approved