A083538 a(n) = sigma(n)*sigma(n+1)/gcd(sigma(n+1), sigma(n))^2.

3, 12, 28, 42, 2, 6, 120, 195, 234, 6, 21, 2, 84, 1, 744, 558, 78, 780, 210, 336, 72, 6, 10, 1860, 1302, 420, 35, 420, 60, 36, 2016, 336, 72, 72, 4368, 3458, 570, 210, 1260, 105, 112, 264, 231, 182, 156, 6, 372, 7068, 589, 744, 1764, 1323, 180, 15, 15, 6, 72, 6, 70

Offset: 1

Author

Labos Elemer, May 21 2003

Keywords

• nonn

Comments

a(n) = A060781(n)/A060780(n) = A083539(n)/A060780(n)^2; quotient when lcm(sigma(n+1), sigma(n)) is divided by gcd(sigma(n+1), sigma(n)).

Examples

			n=10: sigma(10)=18, sigma(11)=12, lcm(18, 12)=36, gcd(18, 12)=6, a(10) = 36/6 = 6.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A066813, A058515, A000203, A060781, A060780, A083539.

Programs

Mathematica

f[x_] := DivisorSigma[1, x] t=Table[LCM[f[w+1], f[w]]/GCD[f[w+1], f[w]], {w, 1, 128}]
Times@@#/(GCD@@#)^2&/@Partition[DivisorSigma[1,Range[60]],2,1] (* Harvey P. Dale, Feb 17 2016 *)

PARI

a(n)=my(x=sigma(n),y=sigma(n+1)); x*y/gcd(x,y)^2 \\ Charles R Greathouse IV, Mar 09 2014

Extensions

Edited by N. J. A. Sloane, Apr 29 2007

Corrections by Charles R Greathouse IV, Mar 09 2014