OFFSET
0,2
COMMENTS
A000540(n) is divisible by A000330(n) if and only if n is congruent to {1,2,4,5} mod 7 (see A047380).
This sequence is the case when n is congruent to 1 mod 7.
A134159 is the case when n is congruent to 2 mod 7.
A134160 is the case when n is congruent to 4 mod 7.
A134161 is the case when n is congruent to 5 mod 7.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = (3(7n + 1)^4 + 6(7n + 1)^3 - 3 (7n + 1) + 1)/7.
a(n) = (Sum_{k=1..7n+1} k^6) / (Sum_{k=1..7n+1} k^2).
G.f.: -(1 + 2186*x + 13638*x^2 + 8498*x^3 + 373*x^4)/(-1+x)^5. - R. J. Mathar, Nov 14 2007
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>4. - Colin Barker, Aug 12 2017
MATHEMATICA
Table[(3(7n + 1)^4 + 6(7n + 1)^3 - 3 (7n + 1) + 1)/7, {n, 0, 100}] (* or *) Table[Sum[k^6, {k, 1, 7n + 1}]/Sum[k^2, {k, 1, 7n + 1}], {n, 0, 100}] (* Artur Jasinski *)
PROG
(PARI) Vec((1 + 2186*x + 13638*x^2 + 8498*x^3 + 373*x^4) / (1 - x)^5 + O(x^30)) \\ Colin Barker, Aug 12 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Artur Jasinski, Oct 10 2007
STATUS
approved