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A337806
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Numbers that are a divisor of the product of the differences of its consecutive divisors.
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2
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8, 12, 16, 20, 24, 27, 28, 30, 32, 36, 40, 44, 45, 48, 52, 56, 60, 63, 64, 68, 70, 72, 76, 80, 81, 84, 88, 90, 92, 96, 99, 100, 104, 105, 108, 112, 116, 117, 120, 124, 125, 126, 128, 132, 135, 136, 140, 144, 148, 150, 152, 153, 154, 156, 160, 164, 165, 168, 171, 172, 175, 176, 180, 182, 184
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OFFSET
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1,1
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LINKS
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EXAMPLE
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8 is a term as the divisors of 8 are 1,2,4,8, the differences of which are 1,2,4, and 1*2*4 = 8 which is a multiple of 8.
20 is a term as the divisors of 20 are 1,2,4,5,10,20, the differences of which are 1,2,1,5,10, and 1*2*1*5*10 = 100 which is a multiple of 20.
27 is a term as the divisors of 27 are 1,3,9,27, the differences of which are 2,6,18, and 2*6*18 = 216 which is a multiple of 27.
99 is a term as the divisors of 99 are 1,3,9,11,33,99, the difference of which are 2,6,2,22,66, and 2*6*2*22*66 = 34848 which is a multiple of 99.
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MAPLE
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filter:= proc(n) local R, p;
R:= sort(convert(numtheory:-divisors(n), list));
p:= convert(R[2..-1]-R[1..-2], `*`);
p mod n = 0
end proc:
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MATHEMATICA
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Select[Range[2, 200], Divisible[Times @@ Differences @ Divisors[#], #] &] (* Amiram Eldar, Sep 23 2020 *)
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PROG
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(PARI) isok(k) = my(d=divisors(k)); (#d > 1) && (vecprod(vector(#d-1, k, d[k+1]-d[k])) % k) == 0; \\ Michel Marcus, Sep 23 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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STATUS
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approved
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