OFFSET
1,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 3000 terms from Eric Desbiaux)
FORMULA
EXAMPLE
MAPLE
a:= n-> add(combinat[numbpart](i[1])*i[2], i=ifactors(n)[2]):
seq(a(n), n=1..70); # Alois P. Heinz, Mar 17 2021
MATHEMATICA
{0}~Join~Array[Total@ Map[#2 PartitionsP[#1] & @@ # &, FactorInteger[#]] &, 58, 2] (* Michael De Vlieger, Mar 17 2021 *)
PROG
(Sage)
def a(n):
return sum([Partitions(primefactor).cardinality() for (primefactor, exponent) in factor(n) for _ in range(exponent)])
[a(n) for n in (1..100)]
(PARI) a(n) = my(f=factor(n)); sum(k=1, #f~, f[k, 2]*numbpart(f[k, 1])); \\ Michel Marcus, Mar 17 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Eric Desbiaux, Mar 16 2021
STATUS
approved