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A307727 Number of partitions of n into 3 prime powers (not including 1). 6
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
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
Sequence in context: A083920 A066508 A319413 * A309081 A333251 A334869
KEYWORD
nonn,look
AUTHOR
Ilya Gutkovskiy, Apr 24 2019
STATUS
approved

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Last modified September 21 02:47 EDT 2023. Contains 365486 sequences. (Running on oeis4.)