A384869 For n >= 1, a(n) = Sum_{k = 1..n} gcd(n, floor((n/k)*10^x)), where x = A121341(k/gcd(n,k)).

1, 3, 7, 8, 17, 21, 31, 27, 53, 33, 71, 58, 85, 74, 103, 75, 129, 118, 145, 70, 209, 141, 199, 146, 197, 194, 309, 191, 281, 175, 301, 206, 427, 271, 339, 297, 397, 306, 503, 157, 481, 432, 505, 336, 559, 395, 553, 388, 607, 303, 777, 454, 677, 620, 605, 467

Offset

1,2

Comments

a(n) < n^2 - n + 1.

Links

Table of n, a(n) for n=1..56.

Example

For n = 12:
k = 4, x = A121341(4/gcd(12,4)) = 0, gcd(12, floor((12/4)*10^0)) = 3;
k = 5, x = A121341(5/gcd(12,5)) = 1, gcd(12, floor((12/5)*10^1)) = 12;
and so on.

Mathematica

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 *)

Crossrefs

Cf. A003592, A018804, A051626, A051628, A085837, A121341.

Sequence in context: A136136 A057548 A122227 * A259571 A291212 A387267

Adjacent sequences: A384866 A384867 A384868 * A384870 A384871 A384872

Keyword

base,nonn

Author

Ctibor O. Zizka, Jun 11 2025

Status

approved