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A213931
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Smallest number k such that the sum of divisors of k equals n times a nontrivial integer power.
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1
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3, 7, 6, 21, 19, 14, 12, 21, 22, 27, 43, 33, 63, 28, 24, 66, 67, 30, 98, 57, 44, 129, 367, 42, 199, 63, 85, 84, 463, 54, 48, 93, 86, 201, 76, 66, 219, 111, 99, 120, 163, 60, 1285, 129, 88, 274, 751, 105, 156, 199, 134, 198, 211, 102, 327, 84, 147, 346, 1765
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OFFSET
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1,1
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COMMENTS
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Smallest k such that sigma(k) = n * m^q where m, q >= 2.
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 1..5000
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EXAMPLE
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a(34) = 201 because sigma(201) = 272 = 34*2^3.
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MAPLE
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with(numtheory):
a:= proc(n) local k, q;
for k while irem(sigma(k), n, 'q')>0 or
igcd(map(i->i[2], ifactors(q)[2])[])<2 do od; k
end:
seq(a(n), n=1..100); # Alois P. Heinz, Jun 26 2012
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MATHEMATICA
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a[n_] := Module[{k, q, r}, For[k = 1, {q, r} = QuotientRemainder[ DivisorSigma[1, k], n]; r>0 || GCD @@ FactorInteger[q][[All, 2]]<2, k++]; k];
Array[a, 100] (* Jean-François Alcover, Nov 21 2020, after Alois P. Heinz *)
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PROG
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(PARI) a(n)=my(k); while(sigma(k++)%n || !ispower(sigma(k)/n), ); k \\ Charles R Greathouse IV, Jun 26 2012
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CROSSREFS
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Cf. A000203, A001597, A213401, A213386, A213420.
Sequence in context: A241016 A245602 A060924 * A213401 A013564 A009467
Adjacent sequences: A213928 A213929 A213930 * A213932 A213933 A213934
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KEYWORD
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nonn
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AUTHOR
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Michel Lagneau, Jun 25 2012
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STATUS
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approved
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