A364391 a(n) = n - (largest nontrivial divisor of n, or 0 if there is none).

1, 2, 3, 2, 5, 3, 7, 4, 6, 5, 11, 6, 13, 7, 10, 8, 17, 9, 19, 10, 14, 11, 23, 12, 20, 13, 18, 14, 29, 15, 31, 16, 22, 17, 28, 18, 37, 19, 26, 20, 41, 21, 43, 22, 30, 23, 47, 24, 42, 25, 34, 26, 53, 27, 44, 28, 38, 29, 59, 30, 61, 31, 42, 32, 52, 33, 67, 34, 46, 35

Offset

1,2

Links

Table of n, a(n) for n=1..70.

Formula

a(n) = n - A032742(n) if n is composite, n otherwise. - Jon E. Schoenfield, Jul 21 2023

Example

The largest nontrivial divisor of 6 is 3, so a(6) = 6 - 3 = 3.

Mathematica

a[n_] := n - If[CompositeQ[n], n/FactorInteger[n][[1, 1]], 0]; Array[a, 100] (* Amiram Eldar, Jul 22 2023 *)

Prog

(Python)
from sympy import isprime, primefactors
def A364391(n): return n if n==1 or isprime(n) else n-n//min(primefactors(n)) # Chai Wah Wu, Aug 20 2023

Crossrefs

Cf. A032742, A060681.

Sequence in context: A363627 A073890 A079311 * A060474 A065988 A335285

Adjacent sequences: A364388 A364389 A364390 * A364392 A364393 A364394

Keyword

nonn

Author

Todor Szimeonov, Jul 21 2023

Status

approved