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Number of ways to write n as n = a*b*c*d with 1 < a <= b <= c <= d < n.
1

%I #15 Nov 09 2018 07:33:21

%S 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,

%T 0,1,0,0,0,1,0,0,0,0,0,0,0,2,0,0,0,0,0,1,0,1,0,0,0,1,0,0,0,2,0,0,0,0,

%U 0,0,0,3,0,0,0,0,0,0,0,2,1,0,0,1,0,0,0,1,0,1,0,0,0,0,0,4

%N Number of ways to write n as n = a*b*c*d with 1 < a <= b <= c <= d < n.

%C This sequence is different from A101638.

%C If p is prime, a(p^k) = A026810(k). - _Robert Israel_, Nov 08 2018

%H Robert Israel, <a href="/A321379/b321379.txt">Table of n, a(n) for n = 1..10000</a>

%e 16 = 2*2*2*2. So a(16) = 1.

%e 24 = 2*2*2*3. So a(24) = 1.

%p N:= 100: # for a(1)..a(N)

%p V:= Vector(N):

%p for a from 2 to floor(N^(1/4)) do

%p for b from a to floor((N/a)^(1/3)) do

%p for c from b to floor((N/a/b)^(1/2)) do

%p for d from c to N/(a*b*c) do

%p V[a*b*c*d]:= V[a*b*c*d]+1

%p od od od od:

%p convert(V,list); # _Robert Israel_, Nov 08 2018

%Y Cf. A026810, A122179, A218320.

%K nonn

%O 1,48

%A _Seiichi Manyama_, Nov 08 2018