Basic Examples 
(2)
 

Here is an illustrative example. Start with the integer partitions of 3:
In[76]:=
IntegerPartitions@3
Out[76]=
{{3},{2,1},{1,1,1}}
Here are their smallest parts:
In[77]:=
Min/@IntegerPartitions@3
Out[77]=
{3,1,1}
Compute the number of smallest parts per partition:
In[78]:=
Count[#,Min[#]]&/@IntegerPartitions@3
Out[78]=
{1,1,3}
Find their total:
In[67]:=
Total@%
Out[67]=
5
This is precisely the value returned by
SmallestPartsFunction
:
[◼]
SmallestPartsFunction
[3]
Out[62]=
5
———
Here are the first 10 numbers in the smallest part function (denoted
spt
) sequence (OEIS A092269):
[◼]
SmallestPartsFunction
/@Range@10
Out[68]=
{1,3,5,10,14,26,35,57,80,119}

Neat Examples 
(3)
 
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