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A316228 Numbers whose Fermi-Dirac prime factorization sums to a Fermi-Dirac prime. 1
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..65.

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: A154799 A020660 A047306 * A283970 A121166 A249017

Adjacent sequences:  A316225 A316226 A316227 * A316229 A316230 A316231

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 27 2018

STATUS

approved

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Last modified January 26 20:33 EST 2020. Contains 331288 sequences. (Running on oeis4.)