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!)
A258429 Primes p such that p - 1 = (tau(p - 1) - 1)^k for some k >= 0, where tau(n) is the number of divisors of n (A000005). 3
2, 5, 17, 65537 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecture: the sequence is finite.

Corresponding values of numbers k: 0, 2, 2, 4, ...

A fermat prime from A019434 of the form F(n) = 2^(2^n) + 1 is a term if k = 2^n * log(2) / log(2^n) is an integer.

LINKS

Table of n, a(n) for n=1..4.

EXAMPLE

65537 (prime) is in the sequence because 65537 - 1 = (tau(65536) - 1)^4 = 16^4.

PROG

(MAGMA) [2] cat [n+1: n in [A219338(n)] | IsPrime(n+1)]

(MAGMA) Set(Sort([n: n in[1..1000000], k in [0..100] | IsPrime(n) and (n-1) eq (NumberOfDivisors(n-1) - 1)^k]))

(PARI) listp(nn) = {print1(p=2, ", "); forprime(p=5, nn, expo = valuation(x=(p-1), y=(numdiv(p-1)-1)); if (x == y^expo, print1(p, ", ")); ); } \\ Michel Marcus, Jun 04 2015

CROSSREFS

Cf. A000005, A019434, A219338, A007516, A004249, A249759.

Sequence in context: A124374 A113617 A226069 * A117839 A269665 A080689

Adjacent sequences:  A258426 A258427 A258428 * A258430 A258431 A258432

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, May 29 2015

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 21 19:57 EDT 2020. Contains 337273 sequences. (Running on oeis4.)