A304634 Numbers n with prime omicron 2, meaning A304465(n) = 2.

4, 6, 9, 10, 12, 14, 15, 18, 20, 21, 22, 24, 25, 26, 28, 33, 34, 35, 36, 38, 39, 40, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 65, 68, 69, 72, 74, 75, 76, 77, 80, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100, 104

Offset: 1

Author

Gus Wiseman, May 15 2018

Keywords

• nonn

Comments

If n > 1 is not a prime number, we have A056239(n) >= Omega(n) >= omega(n) >= A071625(n) >= ... >= omicron(n) > 1 where Omega = A001222, omega = A001221, and omicron = A304465.

Examples

			This is a list of normalized factorizations (see A112798) of selected entries:
    4: {1,1}
    6: {1,2}
   12: {1,1,2}
   24: {1,1,1,2}
   36: {1,1,2,2}
   48: {1,1,1,1,2}
   60: {1,1,2,3}
   72: {1,1,1,2,2}
   96: {1,1,1,1,1,2}
  120: {1,1,1,2,3}
  144: {1,1,1,1,2,2}
  180: {1,1,2,2,3}
  192: {1,1,1,1,1,1,2}
  216: {1,1,1,2,2,2}
  240: {1,1,1,1,2,3}
  288: {1,1,1,1,1,2,2}
  384: {1,1,1,1,1,1,1,2}
  420: {1,1,2,3,4}
  432: {1,1,1,1,2,2,2}
  480: {1,1,1,1,1,2,3}
  576: {1,1,1,1,1,1,2,2}
  768: {1,1,1,1,1,1,1,1,2}
  840: {1,1,1,2,3,4}
  864: {1,1,1,1,1,2,2,2}
  960: {1,1,1,1,1,1,2,3}
		

Crossrefs

Cf. A001221, A001222, A001358, A005117, A007774, A007916, A055932, A071625, A112798, A181819, A182850, A182857, A275870, A304464, A304465, A304636, A304647.

Programs

Mathematica

Join@@Position[Table[Switch[n,1,0,?PrimeQ,1,,NestWhile[Sort[Length/@Split[#]]&,Sort[Last/@FactorInteger[n]],Length[#]>1&]//First],{n,100}],2]