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A307727 Number of partitions of n into 3 prime powers (not including 1). 4
0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 3, 4, 5, 6, 6, 8, 7, 9, 9, 10, 10, 12, 11, 14, 13, 14, 13, 16, 13, 18, 15, 18, 16, 20, 18, 23, 20, 25, 23, 26, 22, 28, 23, 30, 23, 30, 23, 32, 26, 32, 27, 34, 28, 37, 28, 36, 29, 40, 31, 43, 28, 42, 32, 44, 32, 46, 32, 46, 35, 46, 35, 50, 34, 51, 37, 53, 36, 59, 36, 57, 41 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,9

LINKS

Robert Israel, Table of n, a(n) for n = 0..1000

Index entries for sequences related to partitions

FORMULA

a(n) = [x^n y^3] Product_{k>=1} 1/(1 - y*x^A246655(k)).

a(n) = Sum_{j=1..floor(n/3)} Sum_{i=j..floor((n-j)/2)} [omega(i) * omega(j) * omega(n-i-j) == 1], where omega(n) is the number of distinct prime factors of n and [==] is the Iverson bracket. - Wesley Ivan Hurt, Apr 25 2019

EXAMPLE

a(11) = 4 because we have [7, 2, 2], [5, 4, 2], [5, 3, 3] and [4, 4, 3].

MAPLE

f:= proc(n, k, pmax) option remember;

  local t, p, j;

  if n = 0 then return `if`(k=0, 1, 0) fi;

  if k = 0 then return 0 fi;

  if n > k*pmax then return 0 fi;

  t:= 0:

  for p in A246655 do

    if p > pmax then return t fi;

    t:= t + add(procname(n-j*p, k-j, min(p-1, n-j*p)), j=1..min(k, floor(n/p)))

  od;

  t

end proc:

seq(f(n, 3, n), n=0..80) # Robert Israel, Apr 25 2019

MATHEMATICA

Array[Count[IntegerPartitions[#, {3}], _?(AllTrue[#, PrimePowerQ] &)] &, 81, 0]

CROSSREFS

Cf. A000961, A023894, A068307, A246655, A280243, A307726.

Sequence in context: A083920 A066508 A319413 * A309081 A326694 A053207

Adjacent sequences:  A307724 A307725 A307726 * A307728 A307729 A307730

KEYWORD

nonn,look

AUTHOR

Ilya Gutkovskiy, Apr 24 2019

STATUS

approved

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Last modified October 16 03:37 EDT 2019. Contains 328040 sequences. (Running on oeis4.)