OFFSET
1,1
COMMENTS
Primes p such that tau(p+1) = tau(p-1) where tau(k) = A000005(k).
These are the primes in sequence A067888 of numbers n such that tau(n+1) = tau(n-1). - M. F. Hasler, Aug 06 2015
LINKS
T. D. Noe, Table of n, a(n) for n=1..10000
FORMULA
a(n) seems curiously to be asymptotic to 25*n*log(n). [From the number of terms up to 10^8, 10^9, 10^10 and 10^11, i.e., 306147, 2616930, 22835324 and 202105198, this constant can be estimated by 25.858..., 25.858..., 25.845... and 25.872..., respectively. - Amiram Eldar, Jun 28 2022]
EXAMPLE
7 is a member as 6 and 8 both have 4 divisors; 19 is a member as 18 and 20 both have 6 divisors each.
MAPLE
with(numtheory):j := 0:for i from 1 to 10000 do b := ithprime(i): if nops(divisors(b-1))=nops(divisors(b+1)) then j := j+1:a[j] := b:fi:od:seq(a[k], k=1..j);
MATHEMATICA
Prime[ Select[ Range[ 700 ], Length[ Divisors[ Prime[ #1 ] - 1 ]] == Length[ Divisors[ Prime[ #1 ] + 1 ]] & ]]
Select[Prime[Range[1000]], DivisorSigma[0, #-1]==DivisorSigma[0, #+1]&] (* Harvey P. Dale, Jun 08 2018 *)
PROG
(PARI) is_A067889(p)=numdiv(p-1)==numdiv(p+1)&&isprime(p) \\ M. F. Hasler, Jul 31 2015
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Mar 02 2002
STATUS
approved