OFFSET
1,16
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
The a(1152) = 7 factorizations are (4*4*8*9), (4*8*36), (4*9*32), (8*9*16), (8*144), (9*128), (32*36).
MAPLE
ispp:= proc(n) local F;
F:= ifactors(n)[2];
igcd(op(map(t -> t[2], F)))>1
end proc:
f:= proc(n) local F, np, Q;
F:= map(t -> t[2], ifactors(n)[2]);
np:= mul(ithprime(i)^F[i], i=1..nops(F));
Q:= select(ispp, numtheory:-divisors(np));
G(Q, np)
end proc:
G:= proc(Q, n) option remember; local q, t, k;
if not numtheory:-factorset(n) subset `union`(seq(numtheory:-factorset(q), q=Q)) then return 0 fi;
q:= Q[1]; t:= 0;
for k from 0 while n mod q^k = 0 do
t:= t + procname(Q[2..-1], n/q^k)
od;
t
end proc:
G({}, 1):= 1:
map(f, [$1..200]); # Robert Israel, May 06 2018
MATHEMATICA
ppQ[n_]:=And[n>1, GCD@@FactorInteger[n][[All, 2]]>1];
facsp[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facsp[n/d], Min@@#>=d&]], {d, Select[Divisors[n], ppQ]}]];
Table[Length[facsp[n]], {n, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 05 2018
STATUS
approved