cp's OEIS Frontend

A181087 Partitions of n in the order of increasing smallest numbers of prime signatures.

%I A181087 #30 Mar 08 2020 00:05:28
%S A181087 1,2,1,1,3,1,2,4,1,3,1,1,1,5,2,2,1,4,1,1,2,6,2,3,1,5,1,1,3,7,2,4,1,2,
%T A181087 2,1,6,1,1,1,1,3,3,1,1,4,8,2,5,1,2,3,1,7,1,1,1,2,3,4,1,1,5,9,2,6,1,2,
%U A181087 4,1,8,1,1,1,3,3,5,2,2,2,1,1,6,10,1,3,3,2,7,1,1,2,2,4,4,1,2,5,1,9,1,1,1,4,3,6,2,2,3,1,1,7,11,1,3,4,2,8,1,1
%N A181087 Partitions of n in the order of increasing smallest numbers of prime signatures.
%C A181087 The parts of each partition are listed in increasing order.
%H A181087 Alois P. Heinz, <a href="/A181087/b181087.txt">Table of n, a(n) for n = 1..18132</a>
%e A181087 Smallest number with prime signature [1,1,1] is 2^1*3^1*5^1 = 30, the smallest number for [4] is 2^4 = 16, and thus [4] < [1,1,1] in this order.
%e A181087 First partitions in the order of increasing smallest numbers of prime signatures are: [1], [2], [1,1], [3], [1,2], [4], [1,3], [1,1,1], [5], [2,2], [1,4], [1,1,2], [6], [2,3], [1,5], [1,1,3], [7], [2,4], ...
%e A181087 Smallest numbers with these prime signatures are:  2, 4, 6, 8, 12, 16, 24, 30, 32, 36, 48, 60, 64, 72, 96, 120, 128, 144, ... A025487
%t A181087 DeleteDuplicates[Map[Sort[Map[Last, FactorInteger[#]]] &, Range[1000]]] // Grid (* _Geoffrey Critzer_, Nov 27 2015 *)
%o A181087 (Sage)
%o A181087 def A181087_build(w):
%o A181087     seen = set()
%o A181087     a = []
%o A181087     for n in PositiveIntegers():
%o A181087         psig = tuple(sorted(m for p,m in factor(n)))
%o A181087         if psig not in seen:
%o A181087             a.extend(psig)
%o A181087             seen.add(psig)
%o A181087             if len(a) >= w: return a  # _D. S. McNeil_, Jan 23 2011
%Y A181087 Cf. A036036, A036037, A080576, A025487, A095904.
%K A181087 nonn,look
%O A181087 1,2
%A A181087 _Alois P. Heinz_, Jan 23 2011