login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A343733 Primes p at which tau(p^p) is a prime power, where tau is the number-of-divisors function A000005. 0
2, 3, 7, 31, 127, 8191, 131071, 524287, 2147483647, 2305843009213693951, 618970019642690137449562111, 162259276829213363391578010288127, 170141183460469231731687303715884105727 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For every prime p, p^p has p+1 divisors. p=2 is a term, but for all odd primes, p+1 is even, so this sequence consists of 2 and the primes of the form 2^j - 1, i.e., 2 and the Mersenne primes (A000668).

LINKS

Table of n, a(n) for n=1..13.

EXAMPLE

2^2 has 3 = 3^1 divisors, so 2 is a term.

3^3 has 4 = 2^2 divisors, so 3 is a term.

5^5 has 6 = 2*3 divisors, so 5 is not a term.

CROSSREFS

Cf. A000005, A000668, A000312, A062319.

Sequence in context: A089359 A239892 A267487 * A081947 A046972 A006862

Adjacent sequences:  A343730 A343731 A343732 * A343734 A343735 A343736

KEYWORD

nonn,hard

AUTHOR

Jon E. Schoenfield, Jun 01 2021

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 27 08:39 EDT 2021. Contains 347689 sequences. (Running on oeis4.)