A338281 a(n) is the sum of n and the largest proper divisor of n.

3, 4, 6, 6, 9, 8, 12, 12, 15, 12, 18, 14, 21, 20, 24, 18, 27, 20, 30, 28, 33, 24, 36, 30, 39, 36, 42, 30, 45, 32, 48, 44, 51, 42, 54, 38, 57, 52, 60, 42, 63, 44, 66, 60, 69, 48, 72, 56, 75, 68, 78, 54, 81, 66, 84, 76, 87, 60, 90, 62, 93, 84, 96, 78, 99, 68

Offset

2,1

Comments

Contains no primes except for a(2)=3. Contains every number of the form p+1 for prime p (that is, every element of A008864). Contains no powers of 2 except those one more than a Mersenne prime.

Links

Robert Israel, Table of n, a(n) for n = 2..10000

Formula

a(n) = n + A032742(n).

a(2*n) = A008585(n).

Example

For n=2, a(n) = 2+1 = 3.
For n=6, a(n) = 6+3 = 9.

Maple

f:= n -> n *(1+1/min(numtheory:-factorset(n))):
map(f, [$2..100]); # Robert Israel, Oct 28 2020

Mathematica

a[n_] := n + n/FactorInteger[n][[1, 1]]; Array[a, 100, 2] (* Amiram Eldar, Oct 21 2020 *)

Prog

(Python)
def a(n):
    if(n<4):
        return 1+n
    i=2
    while (n%i!=0):
        if i*i>n:
            return 1+n
        i+=1
    return (n//i)+n

Crossrefs

Cf. A008585 (3*n), A008864, A032742.

Equals A166250(n) + 1.

Sequence in context: A162625 A033095 A158907 * A338723 A175708 A373709

Adjacent sequences: A338278 A338279 A338280 * A338282 A338283 A338284

Keyword

nonn

Author

Allen G. Liu, Oct 21 2020

Status

approved