OFFSET
1,2
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(5) = 16 subsets:
{1} {2} {3} {4} {5} {6} {7}
{1,2} {1,3} {1,4} {1,5} {1,6} {1,7}
{2,4} {4,5} {2,6} {4,7}
{3,4} {1,4,5} {3,6} {6,7}
{1,2,4} {4,6} {1,4,7}
{1,3,4} {5,6} {1,6,7}
{1,2,6} {4,6,7}
{1,3,6} {1,4,6,7}
{1,4,6}
{1,5,6}
{2,4,6}
{3,4,6}
{4,5,6}
{1,2,4,6}
{1,3,4,6}
{1,4,5,6}
MATHEMATICA
prisig[n_]:=If[n==1, {}, Sort[Last/@FactorInteger[n]]];
Table[Times@@(1+Length/@Split[Sort[Array[prisig, n]]])/(1+Count[Array[prisig, n], prisig[n]]), {n, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 06 2019
STATUS
approved