|
%I #9 Jul 29 2020 03:29:58
%S 4,9,15,35,39,55,77,95,111,119,183,203,209,215,219,287,299,319,335,
%T 471,527,579,707,767,791,799,815,831,939,959,989,1007,1055,1079,1191,
%U 1199,1211,1263,1343,1371,1415,1623,1655,1691,1703,1799,1829,1839,1967,1983
%N Semiprimes of the form m*k such that (m+1)/(k-1) is prime.
%H Robert Israel, <a href="/A178379/b178379.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1) = 4 because 4 = 2*2 and (2+1)/(2-1) = 3 is prime,
%e a(2) = 9 because 9 = 3*3 and (3+1)/(3-1) = 2 is prime,
%e a(3) = 15 because 15 = 5*3 and (5+1)/(3-1) = 3 is prime,
%e a(4) = 35 because 35 = 7*5 and (7+1)/(5-1) = 2 is prime,
%e a(5) = 39 because 39 = 13*3 and (13+1)/(3-1) = 7 is prime.
%p N:= 2000: # to get all terms <= N
%p P:= select(isprime, [2,seq(i,i=3..N/3,2)]):
%p Res:= NULL:
%p for p in P do qmax:= min(p,N/p);
%p for q in P do
%p if q > qmax then break fi;
%p v:= (p+1)/(q-1);
%p if v::integer and isprime(v) then Res:= Res, q*p fiod od:
%p sort([Res]); # _Robert Israel_, Jul 28 2020
%Y Cf. A000040, A001358.
%K nonn
%O 1,1
%A _Juri-Stepan Gerasimov_, May 26 2010
%E More terms from _R. J. Mathar_, May 28 2010
|
