A167759 Numbers k such that d(k) is an isolated number (A167706).

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, 33, 34, 35, 37, 38, 39, 41, 43, 44, 45, 46, 47, 50, 51, 52, 53, 55, 57, 58, 59, 60, 61, 62, 63, 65, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 79, 82, 83, 84, 85, 86, 87, 89, 90, 91, 92

Offset: 1

Author

Juri-Stepan Gerasimov, Nov 11 2009

Keywords

• nonn

Comments

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.

Examples

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

Crossrefs

Cf. A000005, A002035, A167706.

Programs

Maple

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

Formula

A000005(a(n)) is in A167706.

Extensions

Edited by Jon E. Schoenfield, May 10 2019