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%I #15 Dec 14 2020 19:50:26
%S 0,0,1,0,1,0,1,1,1,1,0,2,0,1,1,1,1,0,1,0,1,0,0,1,1,0,1,1,0,2,0,2,1,2,
%T 2,1,3,0,3,1,2,2,1,2,0,2,0,1,2,0,1,2,0,1,1,1,2,1,2,1,3,1,1,3,1,2,1,2,
%U 1,1,1,0,2,1,0,2,1,0,2,0,3,1,2,3,1,4,0,4,2,3,3,1,4,0,3,1,2,2,0,2,1,1,0,1,1
%N a(n) counts strict partitions of n into powers of 3^t, 5^f and 7^s with positive exponents t, f and s.
%C The sequence is symmetric over several ranges: a(n) = a(2271-n) for n > 84; a(n) = a(16545-n) for n > 920; a(n) = a(68660-n) for n > 9611. (Quote from _Don Reble_: "It's symmetric because 2271 = 3^1 + 3^2 + 3^3 + 3^4 + 3^5 + 3^6 + 5^1 + 5^2 + 5^3 + 5^4 + 7^1 + 7^2 + 7^3. That is, all powers less than 2187 (=3^7) contribute. So for any partition of n, with (2271-2187) < n < 2187, there's a complementary partition for 2271-n.")
%H Fausto A. C. Cariboni, <a href="/A174656/b174656.txt">Table of n, a(n) for n = 1..10000</a>
%e a(100)=2 since 100 = 3 + 3^2 + 3^3 + 5 + 7 + 7^2 and 100 = 3 + 3^2 + 3^4 + 7.
%t n=512;it=Rest@ CoefficientList[Series[ Product[1+x^(3^k),{k,Ceiling[Log[3,n]]}]* Product[1+x^(5^k),{k,Ceiling[Log[5,n]]}]* Product[1+x^(7^k),{k,Ceiling[Log[7,n]]}], {x,0,n}],x]
%K nonn
%O 1,12
%A _Wouter Meeussen_, Mar 25 2010
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