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%I A358903 #20 Feb 14 2024 09:42:51
%S A358903 1,1,1,2,2,2,2,2,3,4,4,4,4,5,7,8,7,9,10,10,10,9,11,15,14,13,15,14,14,
%T A358903 17,16,17,17,16,16,17,17,21,26,24,23,25,27,29,32,31,29,36,36,35,37,37,
%U A358903 42,49,45,44,50,49,50,58,55,55,58,56,58,66,62,65,75
%N A358903 Number of integer partitions of n whose parts have all different numbers of distinct prime factors (A001221).
%H A358903 Alois P. Heinz, <a href="/A358903/b358903.txt">Table of n, a(n) for n = 0..10000</a> (first 101 terms from Lucas A. Brown)
%H A358903 Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A358903.py">Python program</a>.
%e A358903 The a(15) = 8 partitions are: (15), (14,1), (12,3), (12,2,1), (10,5), (10,4,1), (6,9), (8,6,1).
%p A358903 p:= proc(n) option remember; nops(ifactors(n)[2]) end:
%p A358903 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<0, 0,
%p A358903       add((t-> `if`(t<i, b(n-j, t), 0))(p(j)), j=1..n)))
%p A358903     end:
%p A358903 a:= n-> b(n$2):
%p A358903 seq(a(n), n=0..68);  # _Alois P. Heinz_, Feb 14 2024
%t A358903 Table[Length[Select[IntegerPartitions[n],UnsameQ@@PrimeNu/@#&]],{n,0,30}]
%Y A358903 Counting prime factors with multiplicity gives A358901.
%Y A358903 The weakly decreasing version is A358902, with multiplicity A358335.
%Y A358903 A001222 counts prime factors, distinct A001221.
%Y A358903 A116608 counts partitions by sum and number of distinct parts.
%Y A358903 A358836 counts multiset partitions with all distinct block sizes.
%Y A358903 Cf. A046660, A071625, A129519, A141199, A319169, A358831, A358909, A358911.
%K A358903 nonn
%O A358903 0,4
%A A358903 _Gus Wiseman_, Dec 07 2022
%E A358903 a(56) and beyond from _Lucas A. Brown_, Dec 14 2022

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