A330948 Nonprime numbers whose prime indices are not all prime numbers.

4, 6, 8, 10, 12, 14, 16, 18, 20, 21, 22, 24, 26, 28, 30, 32, 34, 35, 36, 38, 39, 40, 42, 44, 46, 48, 49, 50, 52, 54, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 76, 77, 78, 80, 82, 84, 86, 87, 88, 90, 91, 92, 94, 95, 96, 98, 100, 102, 104, 105, 106

Offset

1,1

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.

Links

Table of n, a(n) for n=1..65.

Example

The sequence of terms together with their prime indices of prime indices begins:
   4: {{},{}}
   6: {{},{1}}
   8: {{},{},{}}
  10: {{},{2}}
  12: {{},{},{1}}
  14: {{},{1,1}}
  16: {{},{},{},{}}
  18: {{},{1},{1}}
  20: {{},{},{2}}
  21: {{1},{1,1}}
  22: {{},{3}}
  24: {{},{},{},{1}}
  26: {{},{1,2}}
  28: {{},{},{1,1}}
  30: {{},{1},{2}}
  32: {{},{},{},{},{}}
  34: {{},{4}}
  35: {{2},{1,1}}
  36: {{},{},{1},{1}}
  38: {{},{1,1,1}}

Mathematica

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

Crossrefs

Complement in A330945 of A000040.

Complement in A018252 of A076610.

The restriction to odd terms is A330949.

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

Taking odds instead of nonprimes gives A330946.

The number of prime prime indices is given by A257994.

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

Sequence in context: A201221 A185604 A054023 * A324705 A032583 A175074

Adjacent sequences: A330945 A330946 A330947 * A330949 A330950 A330951

Keyword

nonn

Author

Gus Wiseman, Jan 13 2020

Status

approved