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A252665 Number of ways to write n as n = a*b*c*d*e with 1 <= a <= b <= c <= d <= e <= n. 3
1, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 4, 1, 2, 2, 5, 1, 4, 1, 4, 2, 2, 1, 7, 2, 2, 3, 4, 1, 5, 1, 7, 2, 2, 2, 9, 1, 2, 2, 7, 1, 5, 1, 4, 4, 2, 1, 12, 2, 4, 2, 4, 1, 7, 2, 7, 2, 2, 1, 11, 1, 2, 4, 10, 2, 5, 1, 4, 2, 5, 1, 16, 1, 2, 4, 4, 2, 5, 1, 12, 5, 2, 1, 11, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Starts the same as, but is different from A218320 where a(n) = A218320(n) for n = 1..31. First values of n such that a(n) differs from A218320(n) are 32, 48, 64, 72, 80, ... .

Also starts the same as A001055, but differs from it for n = 64, ...

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-Fran├žois Alcover at A218320 *)

CROSSREFS

Cf. A001055, A034836, A218320.

Sequence in context: A318559 A218320 A305254 * A001055 A320266 A277692

Adjacent sequences:  A252662 A252663 A252664 * A252666 A252667 A252668

KEYWORD

nonn

AUTHOR

Michel Lagneau, Dec 20 2014

STATUS

approved

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Last modified March 18 13:47 EDT 2019. Contains 321289 sequences. (Running on oeis4.)