A124386 - OEIS

A124386

For all n >= 2, Sum_{2<=k<=n, gcd(k,n)>1} a(k) = n. a(1)=1.

1, 2, 3, 2, 5, -1, 7, 5, 7, -3, 11, -3, 13, 5, 7, 9, 17, -15, 19, 7, 11, 3, 23, -15, 9, 17, 33, -3, 29, -55, 31, 77, 47, -15, 45, -89, 37, 91, 79, -45, 41, -171, 43, 183, 189, 37, 47, -351, 155, 123, 373, 165, 53, -655, -471, 533, 553, 191, 59, -859, 61, 861, 233, 33, 839, -1073, 67, 687, 1761, -637, 71

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OFFSET

1,2

LINKS

John Tyler Rascoe, Table of n, a(n) for n = 1..10000

EXAMPLE

The positive integers which are <= 12 and are not coprime to 12 are 2,3,4,6,8,9,10,12. And a(12) is such that a(2)+a(3)+a(4)+a(6)+a(8)+a(9)+a(10)+a(12) = 12.

MATHEMATICA

f[n_] := Select[Range[2, n], GCD[ #, n] > 1 &]; g[l_] := Block[{n = Length[l] + 1}, Append[l, n - Plus @@ l[[Most[f[n]]]]]]; Nest[g, {1}, 70] (* Ray Chandler, Nov 13 2006 *)

PROG

(Python)

from math import gcd

def A124386_list(max_n):

A = [1]

for n in range(2, max_n+1):

A.append(n-sum(A[k-1] for k in range(2, n) if gcd(k, n) > 1))

return A # John Tyler Rascoe, Aug 03 2025

CROSSREFS

Cf. A124385.

Sequence in context: A382941 A053139 A127705 * A098668 A387025 A112763

Adjacent sequences: A124383 A124384 A124385 * A124387 A124388 A124389