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Numbers whose prime indices are not all prime numbers.
18

%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