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%I #20 Aug 29 2019 05:26:26
%S 1,14,2,6,118740,2915640,74322349920
%N Smallest number k such that sigma(k)/sigma(phi(k)) = n.
%C The quotient sigma(k)/sigma(phi(k)) is integral for the numbers in A190503. Does a(n) exist for all n?
%C 10^11 < a(8) <= 11224976029787520. - _Donovan Johnson_, Jun 07 2011
%F a(n)=Min{x; A000203(x)/A000203[A000010(x)]=n}
%e n=6, a(6)=2915640, sigma(2915640)=11793600, phi(2915640)=608256, sigma(608256)=1965600 and 11793600=6*1965600.
%t g[x_] := DivisorSigma[1, x] / DivisorSigma[1, EulerPhi[x]]; m=10; up=200000; a = Table[0, {m}]; Do[ b = g[n]; If[b <= m && IntegerQ[b] && a[[b]] == 0, a[[b]] = n], {n, 1, up} ]; a
%Y Cf. A000203, A000010, A067385, A190503.
%K nonn,more
%O 1,2
%A _Labos Elemer_, Jan 29 2002
%E a(7) from _Donovan Johnson_, Jun 07 2011
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