A077102 Smallest m such that GCD[a+b,a-b]=n, where a=sigma[n],b=phi[n].

4, 1, 18, 21, 200, 14, 3364, 12, 722, 328, 9801, 42, 25281, 116, 1800, 15, 36992, 810, 4414201, 88, 196, 29161, 541696, 35, 2928200, 1413, 103968, 284, 98942809, 488, 1547536, 364, 19602, 17536, 814088, 370, 49042009, 55297, 1521, 440, 3150464641

Offset

1,1

Links

Table of n, a(n) for n=1..41.

Formula

a(n)=Min{x; A077099(x)=n}

Example

n=10,a(10)=328, sigma[328]=630,phi[328]=160, sigma(328)+phi(328)=790, sigma(328)-phi(328)=470, GCD[790,470]=10-n; for n=odd number, a[n] should be either a square or twice a square and so quicker search for large values is possible, like e.g. for n=97:a[97]=m=190077688441=435979^2 is the smallest solution.

Mathematica

f[x_] := Apply[GCD, {DivisorSigma[1, x]+EulerPhi[x], DivisorSigma[1, x]-EulerPhi[x]}] t=Table[0, {100}]; Do[s=f[n]; If[s<101&&t[[s]]==0, t[[s]]=n], {n, 1, 10^13}];

Crossrefs

Cf. A000203, A000010, A077099-A077102, A051612, A065387.

Sequence in context: A331651 A113355 A201201 * A258152 A259051 A192722

Adjacent sequences: A077099 A077100 A077101 * A077103 A077104 A077105

Keyword

nonn

Author

Labos Elemer, Nov 12 2002

Status

approved