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A338405
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a(n) is the smallest number with exactly n divisors d such that sigma(d)/d is an integer.
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2
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1, 6, 84, 672, 3360, 30240, 393120, 12186720, 164989440, 14024102400, 2144862720, 182313331200, 5705334835200, 96990692198400, 187409525022720, 9602078527641600, 124627334140108800, 2118664680381849600, 19067982123436646400, 209747803357803110400, 3985208263798259097600, 63343836614056539340800, 401177631889024749158400, 1203532895667074247475200
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OFFSET
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1,2
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COMMENTS
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a(n) is the smallest number with n multiply-perfect divisors.
Number 1 is only number m such that sigma(d) / d is an integer for all divisors d.
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LINKS
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EXAMPLE
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a(3) = 84 because 84 with divisors 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42 and 84 is the smallest number with 3 multiply-perfect divisors (1, 6 and 28): sigma(1)/1 = 1, sigma(6)/6 = 2, sigma(28)/28 = 2.
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MATHEMATICA
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f[n_] := DivisorSum[n, 1 &, Divisible[DivisorSigma[1, #], #] &]; m = 7; s = Table[0, {m}]; c = 0; n = 1; While[c < m, i = f[n]; If[i <= m && s[[i]] == 0, c++; s[[i]] = n]; n++]; s (* Amiram Eldar, Oct 25 2020 *)
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PROG
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(Magma) [Min([m: m in[1..10^5] | #[d: d in Divisors(m) | IsIntegral(&+Divisors(d) / d)] eq n]): n in [1..6]]
(PARI) a(n) = {my(m=1); while (sumdiv(m, d, !(sigma(d)%d)) != n, m++); m; } \\ Michel Marcus, Oct 25 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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