cp's OEIS Frontend

A330945 Numbers whose prime indices are not all prime numbers.

%I A330945 #7 Jan 14 2020 22:16:59
%S A330945 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 A330945 36,37,38,39,40,42,43,44,46,47,48,49,50,52,53,54,56,57,58,60,61,62,63,
%U A330945 64,65,66,68,69,70,71,72,73,74,76,77,78,79,80,82,84,86,87
%N A330945 Numbers whose prime indices are not all prime numbers.
%C A330945 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 A330945 The sequence of terms together with their prime indices of prime indices begins:
%e A330945    2: {{}}
%e A330945    4: {{},{}}
%e A330945    6: {{},{1}}
%e A330945    7: {{1,1}}
%e A330945    8: {{},{},{}}
%e A330945   10: {{},{2}}
%e A330945   12: {{},{},{1}}
%e A330945   13: {{1,2}}
%e A330945   14: {{},{1,1}}
%e A330945   16: {{},{},{},{}}
%e A330945   18: {{},{1},{1}}
%e A330945   19: {{1,1,1}}
%e A330945   20: {{},{},{2}}
%e A330945   21: {{1},{1,1}}
%e A330945   22: {{},{3}}
%e A330945   23: {{2,2}}
%e A330945   24: {{},{},{},{1}}
%e A330945   26: {{},{1,2}}
%e A330945   28: {{},{},{1,1}}
%e A330945   29: {{1,3}}
%t A330945 Select[Range[100],!And@@PrimeQ/@PrimePi/@First/@If[#==1,{},FactorInteger[#]]&]
%Y A330945 Complement of A076610 (products of primes of prime index).
%Y A330945 Numbers n such that A330944(n) > 0.
%Y A330945 The restriction to odd terms is A330946.
%Y A330945 The restriction to nonprimes is A330948.
%Y A330945 The number of prime prime indices is given by A257994.
%Y A330945 The number of nonprime prime indices is given by A330944.
%Y A330945 Primes of prime index are A006450.
%Y A330945 Primes of nonprime index are A007821.
%Y A330945 Products of primes of nonprime index are A320628.
%Y A330945 The set S of numbers whose prime indices do not all belong to S is A324694.
%Y A330945 Cf. A000040, A000720, A001222, A018252, A056239, A112798, A302242, A320633, A330943, A330947, A330949.
%K A330945 nonn
%O A330945 1,1
%A A330945 _Gus Wiseman_, Jan 13 2020