A104526 Numerator of sum(1/(phi(k)sigma(k)),k=1..n), where phi(k) is the totient function and sigma(k) is the sum of the divisors function.

1, 4, 35, 257, 11, 271, 183, 2773, 36329, 109897, 110443, 27757, 55709, 37291, 49873, 1549703, 13975537, 14010257, 2806565, 2811401, 5631265, 9400487, 103518197, 103642321, 103738417, 311569891, 311818139, 312084119, 312296903, 312607213

Offset: 1

Author

Emeric Deutsch, Mar 12 2005

Keywords

• frac
• nonn

Comments

The first 5 sums are: 1,4/3,35/24,257/168,11/7.

Examples

			a(3)=35 because phi(1)*sigma(1)+phi(2)*sigma(2)+phi(3)*sigma(3)=1/(1*1)+1/(1*3)+1/(2*4)=35/24.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A104527, A093827.

Programs

Maple

with(numtheory): a:=n->numer(sum(1/phi(k)/sigma(k),k=1..n)): seq(a(n),n=1..35);

Mathematica

Accumulate[Table[1/(EulerPhi[n]DivisorSigma[1,n]),{n,30}]]//Numerator (* Harvey P. Dale, Jun 19 2023 *)