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A360093 a(n) is the smallest positive integer which can be represented as the sum of distinct partition numbers in exactly n ways, or -1 if no such integer exists.

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%I A360093 #5 Feb 16 2025 08:34:04
%S A360093 1,3,8,15,18,23,30,33,38,43,45,48,56,58,63,71,74,-1,78,80,85,90,93,
%T A360093 100,101,106,104,109,113,115,119,122,130,-1,134,135,145,141,150,153,
%U A360093 146,149,163,156,158,165,167,173,-1,176,178,182,181,-1,183,186,196,193,191,199
%N A360093 a(n) is the smallest positive integer which can be represented as the sum of distinct partition numbers in exactly n ways, or -1 if no such integer exists.
%H A360093 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PartitionFunctionP.html">Partition Function P</a>, <a href="https://mathworld.wolfram.com/PartitionFunctionQ.html">Partition Function Q</a>
%e A360093 a(5) = 18 because we have [15, 3], [15, 2, 1], [11, 7], [11, 5, 2] and [7, 5, 3, 2, 1].
%Y A360093 Cf. A000041, A280253.
%K A360093 sign
%O A360093 1,2
%A A360093 _Ilya Gutkovskiy_, Jan 25 2023