A162685 Positive integers that are not prime powers and are not divisible by any consecutive primes.

10, 14, 20, 21, 22, 26, 28, 33, 34, 38, 39, 40, 44, 46, 50, 51, 52, 55, 56, 57, 58, 62, 63, 65, 68, 69, 74, 76, 80, 82, 85, 86, 87, 88, 91, 92, 93, 94, 95, 98, 99, 100, 104, 106, 110, 111, 112, 115, 116, 117, 118, 119, 122, 123, 124, 129, 130, 133, 134, 136, 141, 142

Offset: 1

Author

Leroy Quet, Jul 10 2009

Keywords

• nonn

Examples

			220 is factored as 2^2 * 5 * 11. Since both 2 and 5 are not consecutive primes, and 5 and 11 are not consecutive primes (2 and 5 are separated by 3, and 5 and 11 are separated by 7), then 220 is in the sequence.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A073492, A073493.

Cf. A000961, A319630.

Programs

Maple

isA162685 := proc(n) local pfs,i; pfs := numtheory[factorset](n) ; if nops(pfs) <= 1 then RETURN(false) ; else pfs := sort(convert(pfs,list)) ; for i from 2 to nops(pfs) do if op(i,pfs) = nextprime(op(i-1,pfs)) then RETURN(false): fi; od: RETURN(true) ; fi; end: A162685 := proc(n) local a; if n = 1 then 10; else for a from procname(n-1)+1 do if isA162685(a) then RETURN(a) ; fi; od: fi; end: seq(A162685(n),n=1..100) ; # R. J. Mathar, Jul 13 2009

Mathematica

q[n_] := Module[{f = FactorInteger[n]}, Length[f] > 1 && SequenceCount[f[[;; , 1]], {p1_, p2_} /; p2 == NextPrime[p1]] ==  0]; Select[Range[150], q] (* Amiram Eldar, Apr 10 2021 *)

Extensions

More terms from R. J. Mathar, Jul 13 2009