A330948 - OEIS

%I #6 Jan 14 2020 22:17:21

%S 4,6,8,10,12,14,16,18,20,21,22,24,26,28,30,32,34,35,36,38,39,40,42,44,

%T 46,48,49,50,52,54,56,57,58,60,62,63,64,65,66,68,69,70,72,74,76,77,78,

%U 80,82,84,86,87,88,90,91,92,94,95,96,98,100,102,104,105,106

%N Nonprime 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    4: {{},{}}

%e    6: {{},{1}}

%e    8: {{},{},{}}

%e   10: {{},{2}}

%e   12: {{},{},{1}}

%e   14: {{},{1,1}}

%e   16: {{},{},{},{}}

%e   18: {{},{1},{1}}

%e   20: {{},{},{2}}

%e   21: {{1},{1,1}}

%e   22: {{},{3}}

%e   24: {{},{},{},{1}}

%e   26: {{},{1,2}}

%e   28: {{},{},{1,1}}

%e   30: {{},{1},{2}}

%e   32: {{},{},{},{},{}}

%e   34: {{},{4}}

%e   35: {{2},{1,1}}

%e   36: {{},{},{1},{1}}

%e   38: {{},{1,1,1}}

%t Select[Range[100],!PrimeQ[#]&&!And@@PrimeQ/@PrimePi/@First/@If[#==1,{},FactorInteger[#]]&]

%Y Complement in A330945 of A000040.

%Y Complement in A018252 of A076610.

%Y The restriction to odd terms is A330949.

%Y Nonprime numbers n such that A330944(n) > 0.

%Y Taking odds instead of nonprimes gives A330946.

%Y The number of prime prime indices is given by A257994.

%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. A000720, A001222, A056239, A112798, A302242, A320629, A320633, A330943, A330947.

%K nonn

%O 1,1

%A _Gus Wiseman_, Jan 13 2020