This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A385559 #18 Jul 07 2025 11:54:39
%S A385559 1,16,9,32,25,144,49,64,27,400,11,288,13,784,225,128,17,432,19,800,
%T A385559 441,176,23,576,125,208,81,1568,29,3600,31,256,99,272,1225,864,37,304,
%U A385559 117,1600,41,7056,43,352,675,368,47,1152,343,2000,153,416,53,1296,275,3136,171,464,59,7200
%N A385559 Period of {binomial(N,8) mod n: N in Z}.
%H A385559 Jianing Song, <a href="/A385559/b385559.txt">Table of n, a(n) for n = 1..10000</a>
%F A385559 Multiplicative with a(2^e) = 2^(e+3), a(3^e) = 3^(e+1), a(5^e) = 5^(e+1), a(7^e) = 7^(e+1), and a(p^e) = p^e for primes p >= 11.
%F A385559 From _Amiram Eldar_, Jul 07 2025: (Start)
%F A385559 a(n) = n * gcd(210, n) * (4 - 3 * (n mod 2)).
%F A385559 Dirichlet g.f.: zeta(s-1) * (1 + 7/2*(s-1)) * (1 + 2/3*(s-1)) * (1 + 4/5*(s-1)) * (1 + 6/7*(s-1)).
%F A385559 Sum_{k=1..n} a(k) ~ (351/28) * n^2. (End)
%e A385559 For N == 0, 1, ..., 63 (mod 64), binomial(N,8) == {0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 5, 5, 7, 7, 3, 3, 6, 6, 6, 6, 2, 2, 2, 2, 7, 7, 3, 3, 1, 1, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 1, 1, 3, 3, 7, 7, 2, 2, 2, 2, 6, 6, 6, 6, 3, 3, 7, 7, 5, 5, 1, 1} (mod 8).
%t A385559 A385559[n_] := If[n == 1, 1, n*Product[p^Floor[Log[p, 8]], {p, FactorInteger[n][[All, 1]]}]];
%t A385559 Array[A385559, 100] (* _Paolo Xausa_, Jul 07 2025 *)
%t A385559 a[n_] := n * GCD[n, 210] * (4 - 3 * Mod[n, 2]); Array[a, 100] (* _Amiram Eldar_, Jul 07 2025 *)
%o A385559 (PARI) a(n, {choices=8}) = my(r=1, f=factor(n)); for(j=1, #f[, 1], my(p=f[j, 1], e=f[j, 2]); r *= p^(logint(choices, p)+e)); return(r)
%Y A385559 Row n = 8 of A349593. A022998, A385555, A385556, A385557, A385558, and A385560 are respectively rows 2, 3, 4, 5-6, 7, and 9-10.
%K A385559 nonn,easy,mult
%O A385559 1,2
%A A385559 _Jianing Song_, Jul 03 2025