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 A067889 Primes sandwiched between two numbers having same number of divisors. 13
 7, 19, 41, 103, 137, 199, 307, 349, 491, 739, 823, 919, 1013, 1061, 1193, 1277, 1289, 1409, 1433, 1447, 1481, 1543, 1609, 1667, 1721, 1747, 2153, 2357, 2441, 2617, 2683, 2777, 3259, 3319, 3463, 3581, 3593, 3769, 3797, 3911, 3943, 4013, 4217, 4423, 4457 (list; graph; refs; listen; history; text; internal format)
 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) 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], 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 Cf. A067891 (analog with sigma). Sequence in context: A269428 A097240 A097241 * A190821 A100620 A002177 Adjacent sequences:  A067886 A067887 A067888 * A067890 A067891 A067892 KEYWORD easy,nonn AUTHOR Benoit Cloitre, Mar 02 2002 STATUS approved

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Last modified October 20 04:37 EDT 2019. Contains 328247 sequences. (Running on oeis4.)