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A338281
a(n) is the sum of n and the largest proper divisor of n.
2
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
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
KEYWORD
nonn
AUTHOR
Allen G. Liu, Oct 21 2020
STATUS
approved