OFFSET
1,4
COMMENTS
The sorted prime signature (A118914) of a positive integer is the multiset of exponents in its standard factorization into prime numbers.
EXAMPLE
The a(1) = 1 through a(12) = 20 subsets (A = 10, B = 11, C = 12) are the following. The common cardinality of sets in column n is A085089(n).
1 12 13 124 145 1246 1467 12468 12689 1248A 1468B 12468C
134 1346 13468 13689 1289A 148AB 1248AC
1456 14568 15689 1348A 1689B 12689C
14678 16789 1389A 189AB 1289AC
1458A 13468C
1478A 1348AC
1589A 13689C
1789A 1389AC
14568C
1458AC
14678C
1468BC
1478AC
148ABC
15689C
1589AC
16789C
1689BC
1789AC
189ABC
MATHEMATICA
prisig[n_]:=If[n==1, {}, Sort[Last/@FactorInteger[n]]];
Table[Times@@Length/@Split[Sort[Array[prisig, n]]]/Count[Array[prisig, n], prisig[n]], {n, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 06 2019
STATUS
approved