A327685 Nonprime numbers whose prime indices have a common divisor > 1.

9, 21, 25, 27, 39, 49, 57, 63, 65, 81, 87, 91, 111, 115, 117, 121, 125, 129, 133, 147, 159, 169, 171, 183, 185, 189, 203, 213, 235, 237, 243, 247, 259, 261, 267, 273, 289, 299, 301, 303, 305, 319, 321, 325, 333, 339, 343, 351, 361, 365, 371, 377, 387, 393, 399

Offset: 1

Author

Gus Wiseman, Sep 22 2019

Keywords

• nonn

Comments

First differs from A322336 in lacking 2535 = prime(2)*prime(3)*prime(6)^2.

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. Heinz numbers of integer partitions with a common divisor > 1 are A318978, and the enumeration of these partitions by sum is A108572.

Examples

			The sequence of terms together with their prime indices begins:
    9: {2,2}
   21: {2,4}
   25: {3,3}
   27: {2,2,2}
   39: {2,6}
   49: {4,4}
   57: {2,8}
   63: {2,2,4}
   65: {3,6}
   81: {2,2,2,2}
   87: {2,10}
   91: {4,6}
  111: {2,12}
  115: {3,9}
  117: {2,2,6}
  121: {5,5}
  125: {3,3,3}
  129: {2,14}
  133: {4,8}
  147: {2,4,4}
		

Crossrefs

Cf. A000837, A007916, A018783, A056239, A108572, A112798, A289509, A318978, A327407, A327658.

Programs

Mathematica

Select[Range[100],#>1&&!PrimeQ[#]&&GCD@@PrimePi/@First/@FactorInteger[#]>1&]

Formula

Complement of A000040 in A318978.