A330945 Numbers whose prime indices are not all prime numbers.

2, 4, 6, 7, 8, 10, 12, 13, 14, 16, 18, 19, 20, 21, 22, 23, 24, 26, 28, 29, 30, 32, 34, 35, 36, 37, 38, 39, 40, 42, 43, 44, 46, 47, 48, 49, 50, 52, 53, 54, 56, 57, 58, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 73, 74, 76, 77, 78, 79, 80, 82, 84, 86, 87

Offset: 1

Author

Gus Wiseman, Jan 13 2020

Keywords

• nonn

Comments

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.

Examples

			The sequence of terms together with their prime indices of prime indices begins:
   2: {{}}
   4: {{},{}}
   6: {{},{1}}
   7: {{1,1}}
   8: {{},{},{}}
  10: {{},{2}}
  12: {{},{},{1}}
  13: {{1,2}}
  14: {{},{1,1}}
  16: {{},{},{},{}}
  18: {{},{1},{1}}
  19: {{1,1,1}}
  20: {{},{},{2}}
  21: {{1},{1,1}}
  22: {{},{3}}
  23: {{2,2}}
  24: {{},{},{},{1}}
  26: {{},{1,2}}
  28: {{},{},{1,1}}
  29: {{1,3}}
		

Crossrefs

Complement of A076610 (products of primes of prime index).

Numbers n such that A330944(n) > 0.

The restriction to odd terms is A330946.

The restriction to nonprimes is A330948.

The number of prime prime indices is given by A257994.

The number of nonprime prime indices is given by A330944.

Primes of prime index are A006450.

Primes of nonprime index are A007821.

Products of primes of nonprime index are A320628.

The set S of numbers whose prime indices do not all belong to S is A324694.

Cf. A000040, A000720, A001222, A018252, A056239, A112798, A302242, A320633, A330943, A330947, A330949.

Programs

Mathematica

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