A316228 Numbers whose Fermi-Dirac prime factorization sums to a Fermi-Dirac prime.

2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 22, 23, 24, 25, 28, 29, 31, 34, 36, 37, 39, 40, 41, 43, 46, 47, 48, 49, 52, 53, 55, 56, 58, 59, 61, 63, 66, 67, 71, 73, 76, 79, 81, 82, 83, 88, 89, 90, 94, 97, 100, 101, 103, 104, 107, 108, 109, 112

Offset

1,1

Comments

A Fermi-Dirac prime (A050376) is a number of the form p^(2^k) where p is prime and k >= 0. Every positive integer has a unique factorization into distinct Fermi-Dirac primes.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

Sequence of multiarrows in the form "number: sum <= factors" begins:
   2:  2 <= {2}
   3:  3 <= {3}
   4:  4 <= {4}
   5:  5 <= {5}
   6:  5 <= {2,3}
   7:  7 <= {7}
   9:  9 <= {9}
  10:  7 <= {2,5}
  11: 11 <= {11}
  12:  7 <= {3,4}
  13: 13 <= {13}
  14:  9 <= {2,7}
  16: 16 <= {16}
  17: 17 <= {17}
  18: 11 <= {2,9}
  19: 19 <= {19}
  20:  9 <= {4,5}
  22: 13 <= {2,11}
  23: 23 <= {23}
  24:  9 <= {2,3,4}

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)]]]]];
Select[Range[2, 200], Length[FDfactor[Total[FDfactor[#]]]]==1&]

Crossrefs

Cf. A050376, A064547, A100118, A213925, A299757, A305829, A316202, A316210, A316211, A316220.

Sequence in context: A020660 A047306 A332108 * A353935 A348782 A331119

Adjacent sequences: A316225 A316226 A316227 * A316229 A316230 A316231

Keyword

nonn

Author

Gus Wiseman, Jun 27 2018

Status

approved