A330946 Odd numbers whose prime indices are not all prime numbers.

7, 13, 19, 21, 23, 29, 35, 37, 39, 43, 47, 49, 53, 57, 61, 63, 65, 69, 71, 73, 77, 79, 87, 89, 91, 95, 97, 101, 103, 105, 107, 111, 113, 115, 117, 119, 129, 131, 133, 137, 139, 141, 143, 145, 147, 149, 151, 159, 161, 163, 167, 169, 171, 173, 175, 181, 183, 185

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.

Also MM-numbers of multiset partitions whose parts not all singletons (see example).

Examples

			The sequence of terms together with their prime indices of prime indices begins:
   7: {{1,1}}
  13: {{1,2}}
  19: {{1,1,1}}
  21: {{1},{1,1}}
  23: {{2,2}}
  29: {{1,3}}
  35: {{2},{1,1}}
  37: {{1,1,2}}
  39: {{1},{1,2}}
  43: {{1,4}}
  47: {{2,3}}
  49: {{1,1},{1,1}}
  53: {{1,1,1,1}}
  57: {{1},{1,1,1}}
  61: {{1,2,2}}
  63: {{1},{1},{1,1}}
  65: {{2},{1,2}}
  69: {{1},{2,2}}
  71: {{1,1,3}}
  73: {{2,4}}
		

Crossrefs

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

Including even numbers gives A330945.

The restriction to nonprimes is A330949.

Taking nonprimes instead of odds gives A330947.

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 prime index are A076610.

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, A320629, A330943, A330947, A330948.

Programs

Mathematica

Select[Range[1,100,2],!And@@PrimeQ/@PrimePi/@First/@If[#==1,{},FactorInteger[#]]&]