OFFSET
1,1
COMMENTS
LINKS
Paolo P. Lava, Table of n, a(n) for n = 1..100
EXAMPLE
The anti-divisor of 3 is 2, which is prime.
The anti-divisors of 41 are 2, 3, 9, and 27, whose sum is 41, which is prime.
The anti-divisors of 9941 are 2, 3, 9, 47, 59, 141, 337, 423, 2209, and 6627, whose sum is 9857, which is prime.
MAPLE
with(numtheory): P:=proc(q) local a, i, j, n;
for n from 3 to q do if isprime(n) then
i:=0; j:=n; while j mod 2 <> 1 do i:=i+1; j:=j/2; od;
if isprime(sigma(2*n+1)+sigma(2*n-1)+sigma(n/2^i)*2^(i+1)-6*n-2)
then print(n); fi; fi; od; end: P(10^9);
MATHEMATICA
ad[n_] := Cases[Range[2, n - 1], _?(Abs[Mod[n, #] - #/2] < 1 &)]; Select[Prime@ Range@ 1250, PrimeQ[Total@ ad@ #] &] (* Michael De Vlieger, Jul 10 2015 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Paolo P. Lava, Jul 09 2015
STATUS
approved