A380117 a(n) = n - A380118(n).

0, 1, 2, 1, 2, 2, 3, 2, 0, 0, 1, 1, 2, 2, 2, 1, 2, 2, 3, 3, 3, 3, 4, 4, 0, 0, -2, -2, -1, -1, 0, -1, -1, -1, -1, -1, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 3, 3, -3, -3, -3, -3, -2, -2, -2, -2, -2, -2, -1, -1, 0, 0, 0, -1, -1, -1, 0, 0, 0, 0, 1, 1, 2, 2, 2, 2, 2, 2, 3

Offset: 1

Author

Peter Luschny, Jan 30 2025

Keywords

• sign

Comments

Conjecture: The sign of the terms changes infinitely often.

Links

• Peter Luschny, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A380118, A182936.

Programs

Maple

ExpLambda := n -> n / ilcm(op(numtheory[divisors](n) minus {1, n})):
A380118 := proc(n) option remember; ifelse(n = 1, 1,
A380118(n-1) + ExpLambda(n) - ifelse(isprime(n), n, 0)) end:
a := n -> n - A380118(n): seq(a(n), n = 1..79);