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A259548 Numbers divisible only by primes of the form 6*m-1. 3

%I #25 Sep 08 2022 08:46:13

%S 1,5,11,17,23,25,29,41,47,53,55,59,71,83,85,89,101,107,113,115,121,

%T 125,131,137,145,149,167,173,179,187,191,197,205,227,233,235,239,251,

%U 253,257,263,265,269,275,281,289,293,295,311,317,319,347,353,355,359,383

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

%H Charles R Greathouse IV, <a href="/A259548/b259548.txt">Table of n, a(n) for n = 1..10000</a>

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

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

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

%o (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

%Y Subsequence of A007310.

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

%K nonn

%O 1,2

%A _Bruno Berselli_, Jun 30 2015

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)