A350576 a(n) = n/A055874(n) - A055874(n).

0, -1, 2, 0, 4, -1, 6, 2, 8, 3, 10, -1, 12, 5, 14, 6, 16, 3, 18, 8, 20, 9, 22, 2, 24, 11, 26, 12, 28, 7, 30, 14, 32, 15, 34, 5, 36, 17, 38, 18, 40, 11, 42, 20, 44, 21, 46, 8, 48, 23, 50, 24, 52, 15, 54, 26, 56, 27, 58, 4, 60, 29, 62, 30, 64, 19, 66, 32, 68, 33, 70, 14, 72, 35, 74

Offset: 1

Author

Michel Marcus, Jan 07 2022, after a suggestion from Charles Kusniec

Keywords

• sign

Links

• Michel Marcus, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A055874, A350509.

Cf. A005408 (odd numbers), A056737 (another difference n/d-d).

Programs

Mathematica

a[n_] := Module[{k = 1}, While[Divisible[n, k], k++]; k--; n/k - k]; Array[a, 100] (* Amiram Eldar, Jan 07 2022 *)

PARI

a4(n) = my(m=1); while ((n % m) == 0, m++); m - 1; \\ A055874
a(n) = my(x=a4(n)); n/x - x;

Python

def a(n):
    m = 2
    while n%m == 0: m += 1
    return n//(m-1) - (m-1)
print([a(n) for n in range(1, 76)]) # Michael S. Branicky, Jan 07 2022

Formula

a(n) = A350509(n) - A055874(n).

a(n) = n-1 if n is odd.