OFFSET
1,24
COMMENTS
a(n) depends only on prime signature of n (cf. A025487). So a(24) = a(375) since 24 = 2^3*3 and 375 = 3*5^3 both have prime signature (3,1).
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..10000
FORMULA
Dirichlet g.f.: Product_{n is composite}(1+1/n^s).
MAPLE
with(numtheory):
b:= proc(n, k) option remember;
`if`(isprime(n), 0, `if`(n>k, 0, 1)+
add(`if`(d>k or isprime(d), 0, b(n/d, d-1))
, d=divisors(n) minus {1, n}))
end:
a:= n-> b(n$2):
seq(a(n), n=1..120); # Alois P. Heinz, May 26 2013
MATHEMATICA
b[n_, k_] := b[n, k] = If[PrimeQ[n], 0, If[n>k, 0, 1] + Sum[If[d>k || PrimeQ[d], 0, b[n/d, d-1]], {d, Divisors[n] ~Complement~ {1, n}}]];
a[n_] := b[n, n];
Array[a, 120] (* Jean-François Alcover, Mar 21 2017, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Christian G. Bower, Nov 15 1999
STATUS
approved