1,1

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

T. D. Noe, Table of n, a(n) for n=1..10000

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]

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.

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);

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 *)

(PARI) is_A067889(p)=numdiv(p-1)==numdiv(p+1)&&isprime(p) \\ M. F. Hasler, Jul 31 2015

Cf. A067888, A067891 (analog with sigma).

Sequence in context: A269428 A097240 A097241 * A190821 A100620 A002177

Adjacent sequences: A067886 A067887 A067888 * A067890 A067891 A067892

easy,nonn

Benoit Cloitre, Mar 02 2002

approved