A167759 - OEIS

%I #9 May 11 2019 02:06:38

%S 2,3,5,6,7,8,10,11,12,13,14,15,17,18,19,20,21,22,23,26,27,28,29,31,32,

%T 33,34,35,37,38,39,41,43,44,45,46,47,50,51,52,53,55,57,58,59,60,61,62,

%U 63,65,67,68,69,71,72,73,74,75,76,77,79,82,83,84,85,86,87,89,90,91,92

%N Numbers k such that d(k) is an isolated number (A167706).

%C Isolated numbers (A167706) are 2, 4, 6, 12, 18, 23, 30, 37, .... Sequence lists numbers k such that the number of divisors of k is isolated number. Also, the positions of isolated numbers in A000005.

%F A000005(a(n)) is in A167706.

%e A000005(a(1)=2)=2; A000005(a(2)=3)=2; A000005(a(3)=5)=2; A000005(a(4)=6)=4.

%p isA007510 := proc(n) if isprime(n) then not isprime(n+2) and not isprime(n-2) ; else false; end if; end proc: isA014574 := proc(n) isprime(n+1) and isprime(n-1) ; end proc: isA167706 := proc(n) isA007510(n) or isA014574(n) ; end proc: isA167759 := proc(n) isA167706(numtheory[tau](n)) ; end proc: for n from 1 to 100 do if isA167759(n) then printf("%d,",n) ; fi; od: # _R. J. Mathar_, Nov 16 2009

%Y Cf. A000005, A002035, A167706.

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Nov 11 2009

%E Edited by _Jon E. Schoenfield_, May 10 2019