OFFSET
1,4
COMMENTS
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
Michael De Vlieger, Records and first positions of records
EXAMPLE
a(12) = 4 because we can write 12 = 1*1*1*1*12 = 1*1*1*2*6 = 1*1*1*3*4 = 1*1*2*2*3.
MAPLE
with(numtheory):
b:= proc(n, i, t) option remember;
`if`(n=1, 1, `if`(t=1, `if`(n<=i, 1, 0),
add(b(n/d, d, t-1), d=select(x->x<=i, divisors(n)))))
end:
a:= proc(n) local l, m;
l:= sort(ifactors(n)[2], (x, y)-> x[2]>y[2]);
m:= mul(ithprime(i)^l[i][2], i=1..nops(l));
b(m, m, 5)
end:
seq(a(n), n=1..100); # Alois P. Heinz, Aug 31 2017
MATHEMATICA
Table[c=0; Do[If[i<=j<=k<=l<=m && i*j*k*l*m==n, c++], {i, t=Divisors[n]}, {j, t}, {k, t}, {l, t}, {m, t}]; c, {n, 90}]
(* Second program: *)
b[n_, i_, t_] := b[n, i, t] = If[n == 1, 1, If[t == 1, Boole[n <= i], Sum[b[n/d, d, t - 1], {d, Select[Divisors@ n, # <= i &]}]]]; Parallelize@ Array[b[#, #, 5] &@ Apply[Times, Power @@@ Sort[FactorInteger[#], #1[[2]] > #2[[2]] &]] &, 120] (* Michael De Vlieger, Aug 31 2017, after Jean-François Alcover at A218320 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Dec 20 2014
STATUS
approved