A259548 Numbers divisible only by primes of the form 6*m-1.

1, 5, 11, 17, 23, 25, 29, 41, 47, 53, 55, 59, 71, 83, 85, 89, 101, 107, 113, 115, 121, 125, 131, 137, 145, 149, 167, 173, 179, 187, 191, 197, 205, 227, 233, 235, 239, 251, 253, 257, 263, 265, 269, 275, 281, 289, 293, 295, 311, 317, 319, 347, 353, 355, 359, 383

Offset: 1

Author

Bruno Berselli, Jun 30 2015

Keywords

• nonn

Examples

			275 is in sequence because 275 = 5*5*11, where 5 = 6-1 and 11 = 6*2-1.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A007310.

Cf. A004611 (numbers divisible only by primes of the form 6*m+1), A007528.

Programs

Magma

[n: n in [1..400] | forall{d: d in PrimeDivisors(n) | d mod 6 eq 5}];

Mathematica

okQ[n_] := n==1 || And @@ (Mod[#, 6]==5& /@ FactorInteger[n][[All, 1]]); Select[Range[400], okQ] (* Jean-François Alcover, Jul 02 2015 *)

PARI

list(lim)=my(v=List([1]),mn,mx,t); forprime(p=5,lim\=1, if(p%6==5, listput(v,p))); if(lim<25, return(Vec(v))); forprime(p=5,sqrtint(lim), if(p%6<5, next); mx=1; while(v[mx+1]*p<=lim, for(i=mn=mx+1,mx=#v, t=p*v[i]; if(t>lim, break); listput(v,t)))); Set(v) \\ Charles R Greathouse IV, Jan 11 2018