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A303999
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Numbers whose sum of divisors is the seventh power of one of their divisors.
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1
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1, 112890, 120054, 124338, 133998, 137058, 139962, 36705396, 39118548, 52166212, 4661585292, 4677211812, 4851457716, 4968055596, 6168611160, 6232929480, 6236525932, 6261521812, 6311227560, 6362855640, 6430524120, 6468862876, 6488003880, 6500134440, 6506266732
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OFFSET
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1,2
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COMMENTS
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LINKS
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EXAMPLE
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Divisors of 112890 are 1, 2, 3, 5, 6, 10, 15, 30, 53, 71, 106, 142, 159, 213, 265, 318, 355, 426, 530, 710, 795, 1065, 1590, 2130, 3763, 7526, 11289, 18815, 22578, 37630, 56445, 112890 and their sum is 279936 = 6^7.
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MAPLE
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with(numtheory): P:=proc(q) local a, k, n;
for n from 1 to q do a:=sort([op(divisors(n))]);
for k from 1 to nops(a) do if sigma(n)=a[k]^7 then print(n); break; fi; od; od; end: P(10^9);
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MATHEMATICA
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Select[Range[150000], IntegerQ[t = DivisorSigma[1, #]^(1/7)] && Mod[#, t] == 0 &] (* Giovanni Resta, May 04 2018 *)
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PROG
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(PARI) isok(n) = (n==1) || (ispower(s=sigma(n), 7) && !(n % sqrtnint(s, 7))); \\ Michel Marcus, May 05 2018
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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