%I #7 Jan 14 2020 22:16:59
%S 2,4,6,7,8,10,12,13,14,16,18,19,20,21,22,23,24,26,28,29,30,32,34,35,
%T 36,37,38,39,40,42,43,44,46,47,48,49,50,52,53,54,56,57,58,60,61,62,63,
%U 64,65,66,68,69,70,71,72,73,74,76,77,78,79,80,82,84,86,87
%N Numbers whose prime indices are not all prime numbers.
%C A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.
%e The sequence of terms together with their prime indices of prime indices begins:
%e 2: {{}}
%e 4: {{},{}}
%e 6: {{},{1}}
%e 7: {{1,1}}
%e 8: {{},{},{}}
%e 10: {{},{2}}
%e 12: {{},{},{1}}
%e 13: {{1,2}}
%e 14: {{},{1,1}}
%e 16: {{},{},{},{}}
%e 18: {{},{1},{1}}
%e 19: {{1,1,1}}
%e 20: {{},{},{2}}
%e 21: {{1},{1,1}}
%e 22: {{},{3}}
%e 23: {{2,2}}
%e 24: {{},{},{},{1}}
%e 26: {{},{1,2}}
%e 28: {{},{},{1,1}}
%e 29: {{1,3}}
%t Select[Range[100],!And@@PrimeQ/@PrimePi/@First/@If[#==1,{},FactorInteger[#]]&]
%Y Complement of A076610 (products of primes of prime index).
%Y Numbers n such that A330944(n) > 0.
%Y The restriction to odd terms is A330946.
%Y The restriction to nonprimes is A330948.
%Y The number of prime prime indices is given by A257994.
%Y The number of nonprime prime indices is given by A330944.
%Y Primes of prime index are A006450.
%Y Primes of nonprime index are A007821.
%Y Products of primes of nonprime index are A320628.
%Y The set S of numbers whose prime indices do not all belong to S is A324694.
%Y Cf. A000040, A000720, A001222, A018252, A056239, A112798, A302242, A320633, A330943, A330947, A330949.
%K nonn
%O 1,1
%A _Gus Wiseman_, Jan 13 2020