A167759 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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.

LINKS

Table of n, a(n) for n=1..71.

FORMULA

A000005(a(n)) is in A167706.

EXAMPLE

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

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

CROSSREFS

Cf. A000005, A002035, A167706.

Sequence in context: A337533 A028785 A166546 * A028812 A039251 A283296

Adjacent sequences: A167756 A167757 A167758 * A167760 A167761 A167762

KEYWORD

nonn

AUTHOR

Juri-Stepan Gerasimov, Nov 11 2009

EXTENSIONS

Edited by Jon E. Schoenfield, May 10 2019

STATUS

approved