A330947 Nonprime numbers whose prime indices are all prime numbers.

1, 9, 15, 25, 27, 33, 45, 51, 55, 75, 81, 85, 93, 99, 121, 123, 125, 135, 153, 155, 165, 177, 187, 201, 205, 225, 243, 249, 255, 275, 279, 289, 295, 297, 327, 335, 341, 363, 369, 375, 381, 405, 415, 425, 451, 459, 465, 471, 495, 527, 531, 537, 545, 561, 573

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:
    1: {}
    9: {{1},{1}}
   15: {{1},{2}}
   25: {{2},{2}}
   27: {{1},{1},{1}}
   33: {{1},{3}}
   45: {{1},{1},{2}}
   51: {{1},{4}}
   55: {{2},{3}}
   75: {{1},{2},{2}}
   81: {{1},{1},{1},{1}}
   85: {{2},{4}}
   93: {{1},{5}}
   99: {{1},{1},{3}}
  121: {{3},{3}}
  123: {{1},{6}}
  125: {{2},{2},{2}}
  135: {{1},{1},{1},{2}}
  153: {{1},{1},{4}}
  155: {{2},{5}}
		

Crossrefs

Complement in A076610 of A000040.

Complement in A018252 of A330948.

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 prime index are A076610.

Products of primes of nonprime index are A320628.

Numbers whose prime indices are not all prime are A330945.

Cf. A000720, A001222, A056239, A112798, A302242, A320629, A320633, A330949.

Programs

Mathematica

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