A281660 The least common multiple of 1+n and 1+n^2.

1, 2, 15, 20, 85, 78, 259, 200, 585, 410, 1111, 732, 1885, 1190, 2955, 1808, 4369, 2610, 6175, 3620, 8421, 4862, 11155, 6360, 14425, 8138, 18279, 10220, 22765, 12630, 27931, 15392, 33825, 18530, 40495, 22068, 47989, 26030, 56355, 30440, 65641, 35322

Offset: 0

Author

R. J. Mathar, Jan 26 2017

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (0,4,0,-6,0,4,0,-1)

Programs

Maple

A281660 := proc(n)
        ilcm(1+n,1+n^2) ;
end proc:

Formula

a(n) = lcm(1+n,1+n^2) = (1+n)*(1+n^2)/gcd(1+n,1+n^2) = A053698(n)/A000034(n).

G.f.: (5*x^2+1) *(x^4+2*x^3+6*x^2+2*x+1) / ( (x-1)^4 *(1+x)^4 ).

a(2*n+1) = 2*A059722(n+1). - R. J. Mathar, Jan 28 2017

a(n) = ((3 + (-1)^n)*(1+n+n^2+n^3)) / 4. - Colin Barker, Feb 07 2017