%I #7 Nov 16 2021 21:27:06
%S 13,3433,31591,130351,370273,846613,1679323,3013051,5017141,7885633,
%T 11837263,17115463,23988361,32748781,43714243,57226963,73653853,
%U 93386521,116841271,144459103,176705713,214071493,257071531,306245611
%N a(n) = 13 + 165*n + 756*n^2 + 1470*n^3 + 1029*n^4.
%C A000540(n) is divisible by A000330(n) if and only if n is congruent to {1,2,4,5} mod 7 (see A047380). A134158 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. A133180 is the union of A134158 and A134159 and A134160 and A134161.
%F a(n) = (3*(7*n + 2)^4 + 6*(7*n + 2)^3 - 3*(7*n + 2) + 1)/7.
%F a(n) = (Sum_{k=1..7n+2} k^6) / (Sum_{k=1..7n+2} k^2).
%F G.f.: -(13+3368*x+14556*x^2+6596*x^3+163*x^4)/(-1+x)^5. - _R. J. Mathar_, Nov 14 2007
%t Table[(3(7n + 2)^4 + 6(7n + 2)^3 - 3 (7n + 2) + 1)/7, {n, 0, 100}]
%t Table[Sum[k^6, {k, 1, 7n + 2}]/Sum[k^2, {k, 1, 7n + 2}], {n, 0, 100}] (* _Artur Jasinski_ *)
%Y Cf. A000330, A000540, A119617, A134153, A134154, A133180, A134158, A134160, A134161.
%K nonn
%O 0,1
%A _Artur Jasinski_, Oct 10 2007