OFFSET
0,4
COMMENTS
The sorted prime signature (A118914) of a positive integer is the multiset of exponents in its standard factorization into prime numbers.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1000
EXAMPLE
The a(0) = 1 through a(9) = 8 subsets:
{} {1} {12} {12} {124} {124} {1246} {1246} {12468} {12468}
{13} {134} {134} {1346} {1346} {13468} {12689}
{145} {1456} {1456} {14568} {13468}
{1467} {14678} {13689}
{14568}
{14678}
{15689}
{16789}
MATHEMATICA
prisig[n_]:=If[n==1, {}, Sort[Last/@FactorInteger[n]]];
Table[Times@@(Length/@Split[Sort[Array[prisig, n]]]), {n, 0, 30}]
PROG
(PARI) a(n)={if(n==0, 1, my(M=Map()); for(i=1, n, my(f=factor(i)[, 2], s=sum(k=1, #f, x^f[k]), z); mapput(M, s, if(mapisdefined(M, s, &z), z + 1, 1))); vecprod(Mat(M)[, 2]))} \\ Andrew Howroyd, Aug 30 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 06 2019
STATUS
approved