A168270 Squarefree numbers which are also isolated numbers.

2, 6, 23, 30, 37, 42, 47, 53, 67, 79, 83, 89, 97, 102, 113, 127, 131, 138, 157, 163, 167, 173, 211, 223, 233, 251, 257, 263, 277, 282, 293, 307, 317, 331, 337, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 439, 443, 449, 457, 462, 467, 479, 487, 491, 499, 503, 509

Offset: 1

Author

Juri-Stepan Gerasimov, Nov 22 2009

Keywords

• nonn

Crossrefs

Cf. A005117, A167706, A168252.

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:
isA005117 := proc(n) n =1 or numtheory[issqrfree](n) ; end proc:
isA168270 := proc(n) isA005117(n) and isA167706(n) ; end proc:
for n from 1 to 600 do if isA168270(n) then printf("%d,",n) ; fi; od: # R. J. Mathar, Dec 09 2009

Formula

A005117 INTERSECT A167706.

A005117 \ A168252.

Extensions

Corrected (missing terms inserted) by R. J. Mathar, Dec 09 2009