A327905 FDH numbers of pairwise coprime sets.

2, 6, 8, 10, 12, 14, 18, 20, 21, 22, 24, 26, 28, 32, 33, 34, 35, 38, 40, 42, 44, 46, 48, 50, 52, 55, 56, 57, 58, 62, 63, 66, 68, 70, 74, 75, 76, 77, 80, 82, 84, 86, 88, 91, 93, 94, 95, 96, 98, 99, 100, 104, 106, 110, 112, 114, 116, 118, 122, 123, 125, 126, 132

Offset

1,1

Comments

Let f(n) = A050376(n) be the n-th Fermi-Dirac prime. The FDH-number of a strict partition or finite set {y_1,...,y_k} is f(y_1)*...*f(y_k).

We use the Mathematica function CoprimeQ, meaning a singleton is not coprime unless it is {1}.

Links

Table of n, a(n) for n=1..63.

Wolfram Language Documentation, CoprimeQ

Example

The sequence of terms together with their corresponding coprime sets begins:
   2: {1}
   6: {1,2}
   8: {1,3}
  10: {1,4}
  12: {2,3}
  14: {1,5}
  18: {1,6}
  20: {3,4}
  21: {2,5}
  22: {1,7}
  24: {1,2,3}
  26: {1,8}
  28: {3,5}
  32: {1,9}
  33: {2,7}
  34: {1,10}
  35: {4,5}
  38: {1,11}
  40: {1,3,4}
  42: {1,2,5}

Mathematica

FDfactor[n_]:=If[n==1, {}, Sort[Join@@Cases[FactorInteger[n], {p_, k_}:>Power[p, Cases[Position[IntegerDigits[k, 2]//Reverse, 1], {m_}->2^(m-1)]]]]];
nn=100; FDprimeList=Array[FDfactor, nn, 1, Union];
FDrules=MapIndexed[(#1->#2[[1]])&, FDprimeList];
Select[Range[nn], CoprimeQ@@(FDfactor[#]/.FDrules)&]

Crossrefs

Heinz numbers of pairwise coprime partitions are A302696 (all), A302797 (strict), A302569 (with singletons), and A302798 (strict with singletons).

FDH numbers of relatively prime sets are A319827.

Cf. A050376, A056239, A064547, A213925, A259936, A299755, A299757, A304711, A319826, A326675.

Sequence in context: A173634 A005795 A319827 * A157502 A216032 A076300

Adjacent sequences: A327902 A327903 A327904 * A327906 A327907 A327908

Keyword

nonn

Author

Gus Wiseman, Sep 30 2019

Status

approved