Search: id:A056629
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%I A056629
%S A056629 1,1,1,1,1,4,4,4,4,8,8,8,8,16,8,8,8,8,8,16,8,16,16,16,16,32,32,64,64,
%T A056629 64,64,64,32,64,64,64,64,128,64,64,64,64,64,128,128,256,256,256,256,
%U A056629 256,128,256,256,256,256,256,128,256,256,256,256,512,512,512,512,512
%N A056629 Number of unitary square divisors of n!.
%C A056629 Unitary analogue of A046951(n!)=A055993(n).
%F A056629 a(n)=2^r, where r is the number of prime divisors of unitary analogue 
               of largest square divisor of n!. r(n)=A001221[A000188(n!)/A055229(n!)]
%e A056629 n=10 and the largest square-root divisor of 10! is 720. 10! has 30 square 
               divisors, of which 8 is unitary [and squares]: {1,25,81,256,2025,
               6400,20736,518400}. E.g. GCD[256,10!/256]=GCD[256,14175]=1. Thus 
               a(10)=8.
%Y A056629 Cf. A055993, A048656, A056657, A000188, A008833, A055229, A046951, A055230, 
               A055071, A001221.
%Y A056629 Sequence in context: A159835 A047210 A120327 this_sequence A167185 A081676 
               A114555
%Y A056629 Adjacent sequences: A056626 A056627 A056628 this_sequence A056630 A056631 
               A056632
%K A056629 nonn
%O A056629 1,6
%A A056629 Labos E. (labos(AT)ana.sote.hu), Aug 08 2000

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