A242217 Number of partitions of n into distinct Heegner numbers, cf. A003173.
1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 3, 3, 2, 2, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 1, 2, 2, 3, 3, 2, 3, 2, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 3, 2, 2, 3
Offset: 0
Keywords
Examples
a(10) = #{7+3, 7+2+1} = 2;
a(11) = #{11, 7+3+1} = 2;
a(12) = #{11+1, 7+3+2} = 2;
a(13) = #{11+2, 7+3+2+1} = 2;
a(14) = #{11+3, 11+2+1} = 2;
a(15) = #{11+3+1} = 1;
a(16) = #{11+3+2} = 1;
a(17) = #{11+3+2+1} = 1;
a(18) = #{11+7} = 1;
a(19) = #{19, 11+7+1} = 2;
a(20) = #{19+1, 11+7+2} = 2;
a(316) = #{163+67+43+19+11+7+3+2+1} = 1.
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 0..400
- Eric Weisstein's World of Mathematics, Heegner Number
- Wikipedia, Heegner number
Crossrefs
Cf. A242216.
Programs
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Haskell
a242217 = p [1,2,3,7,11,19,43,67,163] where p _ 0 = 1 p [] _ = 0 p (k:ks) m = if m < k then 0 else p ks (m - k) + p ks m
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Mathematica
heegnerNums = {1,2,3,7,11,19,43,67,163}; a[n_] := a[n] = Count[IntegerPartitions[n, All, heegnerNums], P_List /; Sort[P] == Union[P]]; Table[Print[n," ", a[n]]; a[n], {n,0,316}] (* Jean-François Alcover, Jun 10 2019 *)
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