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%I #4 Jan 19 2021 21:27:41
%S 0,0,0,0,1,0,0,0,1,1,2,3,4,5,7,8,10,12,13,15,18,18,22,23,27,28,32,31,
%T 38,37,41,42,49,46,53,51,62,59,70,65,82,73,89,81,99,89,108,96,118,104,
%U 128,114,142,122,153,133,167,142,178,153,195,167,207,176,225,190,243,204
%N Number of partitions of n into 4 parts with the same number of distinct prime factors.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} [omega(k) = omega(j) = omega(i) = omega(n-i-j-k)], where omega is the number of distinct prime factors (A001221) and [ ] is the (generalized) Iverson bracket.
%t Table[Sum[Sum[Sum[KroneckerDelta[PrimeNu[k], PrimeNu[j], PrimeNu[i], PrimeNu[n - i - j - k]], {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 80}]
%Y Cf. A001221 (omega).
%K nonn
%O 0,11
%A _Wesley Ivan Hurt_, Jan 19 2021
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