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 A384869 #49 Jun 26 2025 17:54:15
%S A384869 1,3,7,8,17,21,31,27,53,33,71,58,85,74,103,75,129,118,145,70,209,141,
%T A384869 199,146,197,194,309,191,281,175,301,206,427,271,339,297,397,306,503,
%U A384869 157,481,432,505,336,559,395,553,388,607,303,777,454,677,620,605,467
%N A384869 For n >= 1, a(n) = Sum_{k = 1..n} gcd(n, floor((n/k)*10^x)), where x = A121341(k/gcd(n,k)).
%C A384869 a(n) < n^2 - n + 1.
%e A384869 For n = 12:
%e A384869 k = 4, x = A121341(4/gcd(12,4)) = 0, gcd(12, floor((12/4)*10^0)) = 3;
%e A384869 k = 5, x = A121341(5/gcd(12,5)) = 1, gcd(12, floor((12/5)*10^1)) = 12;
%e A384869 and so on.
%t A384869 f[n_] := Max[IntegerExponent[n, 2], IntegerExponent[n, 5]] + Length[RealDigits[1/n][[1, -1]]]; a[n_] := Sum[GCD[n, Floor[(n/k)*10^f[k/GCD[n, k]]]], {k, 1, n}]; Array[a, 100] (* _Amiram Eldar_, Jun 19 2025 *)
%Y A384869 Cf. A003592, A018804, A051626, A051628, A085837, A121341.
%K A384869 base,nonn
%O A384869 1,2
%A A384869 _Ctibor O. Zizka_, Jun 11 2025