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

1,2

Links

Table of n, a(n) for n=1..39.

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

Example

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}

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[#]&]

Crossrefs

Equal omega: A327900

Equal sum of prime indices: A327901

Equal average of prime indices: A327902

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

Sequence in context: A326256 A210477 A138563 * A092797 A105212 A067875

Adjacent sequences: A327905 A327906 A327907 * A327909 A327910 A327911

Keyword

nonn

Author

Gus Wiseman, Sep 30 2019

Status

approved