A286320 Number of partitions of n into distinct powerful parts (A001694).
1, 1, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 2, 1, 0, 1, 3, 2, 1, 2, 3, 2, 1, 2, 3, 3, 2, 4, 5, 3, 2, 4, 5, 3, 2, 4, 6, 4, 2, 4, 7, 5, 2, 5, 8, 5, 2, 5, 8, 6, 3, 5, 10, 8, 4, 6, 10, 8, 4, 6, 10, 9, 5, 8, 12, 10, 6, 9, 13, 10, 6, 9, 15, 12, 7, 10, 17, 14, 7, 11, 18, 15, 8, 11, 18, 16, 9, 11, 20, 18, 10, 13
Offset: 0
Keywords
Examples
a(25) = 3 because we have [25], [16, 9] and [16, 8, 1].
Links
- Eric Weisstein's World of Mathematics, Powerful Number
- Index entries for sequences related to powerful numbers
- Index entries for sequences related to partitions
Programs
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Mathematica
nmax = 100; CoefficientList[Series[(1 + x) Product[1 + Boole[Min@ FactorInteger[k][[All, 2]] > 1] x^k, {k, 2, nmax}], {x, 0, nmax}], x]