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A134339
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a(n) = product of the positive "non-isolated divisors" of (2n). A divisor, k, of n is non-isolated if (k-1) or (k+1) also divides n.
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2
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2, 2, 6, 2, 2, 24, 2, 2, 6, 40, 2, 24, 2, 2, 180, 2, 2, 24, 2, 40, 252, 2, 2, 24, 2, 2, 6, 112, 2, 720, 2, 2, 6, 2, 2, 1728, 2, 2, 6, 40, 2, 1008, 2, 2, 16200, 2, 2, 24, 2, 40, 6, 2, 2, 24, 220, 112, 6, 2, 2, 720, 2, 2, 252, 2, 2, 3168, 2, 2, 6, 40, 2, 1728, 2, 2, 180, 2, 2, 3744, 2, 40, 6
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OFFSET
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1,1
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COMMENTS
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No odd integer has any non-isolated divisors.
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LINKS
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FORMULA
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EXAMPLE
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The divisors of 2*10 = 20 are 1,2,4,5,10,20. Of these, 1,2,4,5 are the non-isolated divisors. So a(10) = 1*2*4*5 = 40.
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MATHEMATICA
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pnid[n_]:=With[{d=Divisors[2n]}, Times@@Select[d, MemberQ[d, #+1] || MemberQ[ d, #-1]&]]; Array[pnid, 100] (* Harvey P. Dale, Jul 07 2020 *)
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PROG
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(PARI) a(n) = {my(c=1, k=2*n, x=1); fordiv(k, d, if(d==c+1 || k%(d+1)==0, x*=d); c=d); x; } \\ Jinyuan Wang, Mar 12 2020
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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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