A067740 Smallest number k such that sigma(k)/sigma(phi(k)) = n.

1, 14, 2, 6, 118740, 2915640, 74322349920

Offset: 1

Author

Labos Elemer, Jan 29 2002

Keywords

• nonn
• more

Comments

The quotient sigma(k)/sigma(phi(k)) is integral for the numbers in A190503. Does a(n) exist for all n?

10^11 < a(8) <= 11224976029787520. - Donovan Johnson, Jun 07 2011

Examples

			n=6, a(6)=2915640, sigma(2915640)=11793600, phi(2915640)=608256, sigma(608256)=1965600 and 11793600=6*1965600.
		

Crossrefs

Cf. A000203, A000010, A067385, A190503.

Programs

Mathematica

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

Formula

a(n)=Min{x; A000203(x)/A000203[A000010(x)]=n}

Extensions

a(7) from Donovan Johnson, Jun 07 2011