OFFSET
0,2
COMMENTS
If d|(1 + n^2) and d|(1 + n^3), then d|((1 + n^2) - (n*(1 + n^2) - (1 + n^3))^2) = 2*n. If k|n and k|(1 + n^2), then k = 1 is only option since k|n^2 and k|(1 + n^2). So d must be 1 or 2, exactly. Obviously if n is odd, then the greatest d must be 2 since 1 + n^2 and 1 + n^3 are even. If n is even, then d must be 1 since 1 + n^2 and 1 + n^3 are odd.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,6,0,-15,0,20,0,-15,0,6,0,-1).
FORMULA
a(n) = lcm(1+n^2, 1+n^3) = (1+n^2)*(1+n^3)/gcd(1+n^2, 1+n^3).
a(n) = (1+n^2)*(1+n^3)/ A000034(n) with g.f. ( 1 +2*x +39*x^2 +128*x^3 +850*x^4 +828*x^5 +2054*x^6 +832*x^7 +861*x^8 +130*x^9 +35*x^10 ) / ( (x-1)^6 *(1+x)^6 ).
a(n) = (3 + (-1)^n)*(1 + n^2 + n^3 + n^5)/4. - Colin Barker, Feb 07 2017
MAPLE
MATHEMATICA
Table[LCM[n^2+1, n^3+1], {n, 0, 50}] (* Harvey P. Dale, Jun 10 2023 *)
PROG
(PARI) a(n) = lcm(n^2+1, n^3+1); \\ Michel Marcus, Jan 29 2017
(PARI) a(n) = (n^2 + 1)*(n^3 + 1)/(1 + n%2); \\ Altug Alkan, Jan 29 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
R. J. Mathar, Jan 26 2017
STATUS
approved