A327908 Nonprime squarefree numbers whose prime indices all have the same Omega (A001222) and the same sum of prime indices (A056239).

1, 667, 2021, 4331, 5767, 7081, 7663, 11021, 11639, 12091, 13837, 15049, 20413, 23213, 26123, 31553, 34933, 35657, 35723, 37909, 37979, 38021, 41449, 42919, 44197, 45113, 51019, 53531, 58339, 63407, 66013, 70531, 72929, 73373, 73903, 75763, 83411, 87361, 90581

Offset: 1

Author

Gus Wiseman, Sep 30 2019

Keywords

• nonn

Examples

			The sequence of terms together with their prime indices begins:
      1: {}
    667: {9,10}
   2021: {14,15}
   4331: {18,20}
   5767: {21,22}
   7081: {21,25}
   7663: {22,25}
  11021: {27,28}
  11639: {27,30}
  12091: {28,30}
  13837: {26,33}
  15049: {26,35}
  20413: {33,35}
  23213: {34,39}
  26123: {36,40}
  31553: {34,49}
  34933: {42,44}
  35657: {42,45}
  35723: {34,55}
  37909: {39,49}
		

Links

• Gus Wiseman, Sequences counting and ranking multiset partitions whose part lengths, sums, or averages are constant or strict.

Crossrefs

Equal omega: A327900

Equal sum of prime indices: A327901

Equal average of prime indices: A327902

Cf. A001222, A038041, A056239, A112798, A320324, A326574, A327899.

Programs

Mathematica

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[10000],!PrimeQ[#]&&SquareFreeQ[#]&&SameQ@@PrimeOmega/@primeMS[#]&&SameQ@@Total/@primeMS/@primeMS[#]&]