A157354 - OEIS

%I #5 Oct 14 2021 13:34:23

%S 385,805,1265,1645,1771,2065,2585,2905,3245,3619,3745,4543,4565,5405,

%T 5845,5885,6265,6391,6785,7567,7945,8239,9185,9205,9499,9545,9845,

%U 11891,12145,12305,12485,12565,12859,13363,13405,13783,13865,14465,14927

%N Products of 3 distinct safe primes.

%H Charles R Greathouse IV, <a href="/A157354/b157354.txt">Table of n, a(n) for n = 1..10000</a>

%e 385=5*7*11; 5,7 and 11 are safe primes.

%t lst={};Do[If[Plus@@Last/@FactorInteger[n]==3,a=Length[First/@FactorInteger[n]];If[a==3,b=First/@FactorInteger[n];c=b[[1]];d=b[[2]];e=b[[3]];If[PrimeQ[(c-1)/2]&&PrimeQ[(d-1)/2]&&PrimeQ[(e-1)/2],AppendTo[lst,n]]]],{n,7!}];lst

%o (PARI) list(lim)=my(v=List(),P=select(p->isprime(p\2), primes([5,sqrtint(lim\5+1)-1])),p,q,t); for(i=1,#P, p=P[i]; if(p^3>=lim, break); for(j=i+1,#P, q=P[j]; t=p*q; forprime(r=q+4,lim\t, if(isprime(r\2), listput(v,r*t))))); Set(v); \\ _Charles R Greathouse IV_, Oct 14 2021

%Y Subsequence of A007304.

%Y Cf. A001358, A005384, A005385, A006881, A111206, A157342, A157344, A157345, A157346, A157347, A157352, A157353

%K nonn,easy

%O 1,1

%A _Vladimir Joseph Stephan Orlovsky_, Feb 27 2009