OFFSET
1,1
COMMENTS
Conjecture: For n > 1 there is at least one prime in [n, a(n)] exclusive.
a(n) = 2*n when n is prime.
When n = A002620(m), then a(n) = A002620(m+1), i.e., quarter-squares. Oppermann's conjecture states that there is at least one prime in [A002620(m), A002620(m+1)] exclusive.
When n is square, repeated values for a(n) occur at n-1 and n. These values are A002378(sqrt(n)), i.e., oblong numbers.
When n = A002378(m), then a(n) = (m+1)^2.
LINKS
EXAMPLE
When n = 40, the smallest divisor of 40 that is greater than or equal to sqrt(40) is 8 so a(40)=48.
MATHEMATICA
a248835[n_Integer] := n + Min[Select[Divisors[n], # >= Sqrt[n] &]]; a248835 /@ Range[120] (* Michael De Vlieger, Nov 10 2014 *)
PROG
(Sage)
[n+min([x for x in divisors(n) if x>=sqrt(n)]) for n in [1..100]] # Tom Edgar, Oct 15 2014
(PARI) a(n)=fordiv(n, d, if(d^2>=n, return(n+d))) \\ Charles R Greathouse IV, Oct 21 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Bob Selcoe, Oct 15 2014
STATUS
approved