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A277621
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Number of pairs (a,b) such that a*b = n! and d(a) = d(b) with d = A000005 and a <= b.
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1
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1, 1, 0, 1, 0, 1, 1, 1, 0, 5, 3, 5, 5, 13, 11, 11, 11, 13, 45, 105, 136, 105, 165, 332, 492, 501, 482, 684, 720, 1095, 1656, 3273, 3136, 3901, 4948, 6674, 7641, 15047, 12879, 17217, 38901, 75540, 37743, 73594, 84249, 88592, 207324, 403493, 710536, 922853, 662019
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OFFSET
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0,10
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LINKS
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EXAMPLE
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For n = 9, there are 5 pairs (a,b): (384,945), (420,864), (480,756), (540,672), (560,648)
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MAPLE
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a:=proc(n) local S, nf, DD, d, dd:with(numtheory): S:=0:nf:=n!:DD:=divisors(nf):dd:=floor(sqrt(nf)): for d in DD while d <dd do if tau(d)=tau(nf/d) then S:=S +1 end if: end do: S end proc: # only for small n # Leonid Bedratyuk, Apr 16 2017
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MATHEMATICA
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a[n_] := Length@ Select[ Divisors[n!], # <= n!/# && Equal @@ DivisorSigma[0, {#, n!/#}] &]; a /@ Range[0, 20] (* Giovanni Resta, Apr 11 2017 *)
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PROG
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(PARI) a(n)=my(c=0); fordiv(n!, a, my(b=n!/a); if(a>b, break); if( numdiv(a) == numdiv(b), c++)); c
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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