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A321379 Number of ways to write n as n = a*b*c*d with 1 < a <= b <= c <= d < n.

%I A321379 #15 Nov 09 2018 07:33:21
%S A321379 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 A321379 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 A321379 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 A321379 Number of ways to write n as n = a*b*c*d with 1 < a <= b <= c <= d < n.
%C A321379 This sequence is different from A101638.
%C A321379 If p is prime, a(p^k) = A026810(k). - _Robert Israel_, Nov 08 2018
%H A321379 Robert Israel, <a href="/A321379/b321379.txt">Table of n, a(n) for n = 1..10000</a>
%e A321379 16 = 2*2*2*2. So a(16) = 1.
%e A321379 24 = 2*2*2*3. So a(24) = 1.
%p A321379 N:= 100: # for a(1)..a(N)
%p A321379 V:= Vector(N):
%p A321379 for a from 2 to floor(N^(1/4)) do
%p A321379   for b from a to floor((N/a)^(1/3)) do
%p A321379     for c from b to floor((N/a/b)^(1/2)) do
%p A321379       for d from c to N/(a*b*c) do
%p A321379         V[a*b*c*d]:= V[a*b*c*d]+1
%p A321379 od od od od:
%p A321379 convert(V,list); # _Robert Israel_, Nov 08 2018
%Y A321379 Cf. A026810, A122179, A218320.
%K A321379 nonn
%O A321379 1,48
%A A321379 _Seiichi Manyama_, Nov 08 2018