%I #4 Oct 18 2018 08:50:37

%S 49,91,133,161,169,203,247,259,299,301,329,343,361,371,377,427,437,

%T 481,497,511,529,551,553,559,611,623,637,667,679,689,703,707,721,749,

%U 791,793,817,841,851,893,917,923,931,949,959,973,989,1007,1027,1043,1057

%N Composite numbers whose prime indices are also composite.

%C A prime index of n is a number m such that prime(m) divides n.

%e The sequence of terms begins:

%e 49 = prime(4)^2

%e 91 = prime(4)*prime(6)

%e 133 = prime(4)*prime(8)

%e 161 = prime(4)*prime(9)

%e 169 = prime(6)^2

%e 203 = prime(4)*prime(10)

%e 247 = prime(6)*prime(8)

%e 259 = prime(4)*prime(12)

%e 299 = prime(6)*prime(9)

%e 301 = prime(4)*prime(14)

%e 329 = prime(4)*prime(15)

%e 343 = prime(4)^3

%e 361 = prime(8)^2

%e 371 = prime(4)*prime(16)

%e 377 = prime(6)*prime(10)

%e 427 = prime(4)*prime(18)

%e 437 = prime(8)*prime(9)

%e 481 = prime(6)*prime(12)

%e 497 = prime(4)*prime(20)

%e 511 = prime(4)*prime(21)

%e 529 = prime(9)^2

%e 551 = prime(8)*prime(10)

%e 553 = prime(4)*prime(22)

%e 559 = prime(6)*prime(14)

%e 611 = prime(6)*prime(15)

%e 623 = prime(4)*prime(24)

%e 637 = prime(4)^2*prime(6)

%t Select[Range[2,1000],And[OddQ[#],!PrimeQ[#],And@@Not/@PrimeQ/@PrimePi/@First/@FactorInteger[#]]&]

%Y Cf. A000040, A006450, A007821, A018252, A050370, A056239, A076610, A112798, A302242, A302478, A320533, A320628, A320629.

%K nonn

%O 1,1

%A _Gus Wiseman_, Oct 18 2018