

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
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OFFSET

1,1


COMMENTS

Primes p such that tau(p+1)=tau(p1) where tau(k)=A000005(k).
These are the primes in sequence A067888 of numbers n such that tau(n+1)=tau(n1).  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(b1))=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(p1)==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



