OFFSET
1,1
COMMENTS
Does any prime have more than one representation as phi(k) + d(k)?
LINKS
Robert Israel, Table of n, a(n) for n = 1..3000
EXAMPLE
a(4) = 13 is a term because 13 is prime and for k = 16, phi(k) + d(k) = 8 + 5 = 13.
MAPLE
N:= 10^6: # to allow k <= N
pmax:= evalf(N/(exp(gamma)*log(log(N))+3/log(log(N)))): # lower bound for phi(k), k<=N
P:= {3}:
for k from 1 to sqrt(N) do
n:= k^2;
v:= numtheory:-phi(n)+numtheory:-tau(n);
if v <= pmax and isprime(v) then
P:= P union {v};
fi
od:
sort(convert(P, list));
MATHEMATICA
Select[Table[EulerPhi[n]+DivisorSigma[0, n], {n, 400000}], PrimeQ]//Sort (* Harvey P. Dale, Feb 29 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Oct 19 2022
STATUS
approved