OFFSET
1,2
COMMENTS
a(n) = Product_{d|n} dbar^p*(n/d)), with dbar=Product_{i>=1} di, with di=d^(1/i) when d is an i-th power, and di=1 otherwise (see link).
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..1000
V. C. Harris and M. V. Subbarao, On product partitions of integers, Canad. Math. Bull.Vol. 34 (4), 1991 pp. 474-479.
FORMULA
a(n) = n^A001055(n).
MAPLE
g:= proc(n, k) option remember; `if`(n>k, 0, 1)+
`if`(isprime(n), 0, add(`if`(d>k, 0, g(n/d, d)),
d=numtheory[divisors](n) minus {1, n}))
end:
a:= n-> n^g(n$2):
seq(a(n), n=1..45); # Alois P. Heinz, May 16 2014
MATHEMATICA
g[n_, k_] := g[n, k] = If[n > k, 0, 1] + If[PrimeQ[n], 0, Sum[If[d > k, 0, g[n/d, d]], {d, Divisors[n] ~Complement~ {1, n}}]];
a[n_] := n^g[n, n];
Array[a, 45] (* Jean-François Alcover, Mar 27 2017, after Alois P. Heinz *)
PROG
(PARI) fcnt(n, m) = {local(s); s=0; if(n == 1, s=1, fordiv(n, d, if(d > 1 & d <= m, s=s+fcnt(n/d, d)))); s} /*cf A001055 */
a(n) = {for (i=1, n, print1(i^fcnt(i, i), ", "); ); }
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Marcus, Oct 26 2012
STATUS
approved