A213931 Smallest number k such that the sum of divisors of k equals n times a nontrivial integer power.
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
Offset: 1
Keywords
Examples
a(34) = 201 because sigma(201) = 272 = 34*2^3.
Links
- Alois P. Heinz, Table of n, a(n) for n = 1..5000
Programs
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Maple
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 -
Mathematica
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 *) -
PARI
a(n)=my(k);while(sigma(k++)%n || !ispower(sigma(k)/n), ); k \\ Charles R Greathouse IV, Jun 26 2012
Comments