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partitions of primes

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  • echolalie
    part(n) gives the number of ways of writing the integer n as a sum of positive integers, where the order of addends is not considered significant For example
    Message 1 of 1 , Jun 23, 2005
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      part(n) gives the number of ways of writing the integer n as a sum
      of positive integers, where the order of addends is not considered
      significant
      For example :
      part(2) = 2 ( 2= 1+1, 2 = 2)
      part(4) = 5 ( 4=1+1+1+1, 4 = 1+1+2, 4 = 1+3, 4= 2+2, 4= 4)
      part(10) = 42

      I have looked for some primes p where part(p) is prime and found the
      following up to 84017 : (there are not so many)

      p part(p)

      2 2
      3 3
      5 7
      13 101
      157 80630964769
      491 1394313503224447816939
      863 87674799670795146675673859587
      1621 62607220478448273296879161314388228250413
      2633 79074320470247928120049519839632230336234433216761019
      5347 ...
      8117 ...
      13513 ...
      35227 ...
      62311 ...
      76367 ...
      84017
      1372120162673415582806826150062332140456619038340504836071117572690237
      73670204686425
      1678778124054760354588267560482163346180100706058147470789037160575859
      165670205047481551708397149841
      6522090298056371424057896486751045195249317220494084200266976209439665
      078919700196361237857931088937
      7355136119441712633463748576992319

      Does anybody have an idea about this sequence ? (infinite, etc ..)
      thx
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