A070813 Fermat primes minus 3.

0, 2, 14, 254, 65534

Offset: 1

Author

Labos Elemer, May 09 2002

Keywords

• nonn
• more

Comments

Even numbers 2m such that phi(gpf(x)) - gpf(phi(x)) = 2m for some x, where gpf(m) is the largest prime divisor of m and phi(m) = totient(m).

Solutions to A070812(x) = 0 are in A007283, for A070812(x) = 2 are in A070004.

Crossrefs

Cf. A000010, A006530, A019434, A070812, A007283, A070004.

Programs

Mathematica

pf[x_] := Part[Reverse[Flatten[FactorInteger[x]]], 2];
allS = Reap[Do[s=EulerPhi[pf[n]]-pf[EulerPhi[n]]; If[ !OddQ[s]&&Greater[s, 2], Sow[s]], {n, 3, 10^5}]][[-1, 1]]; (* Only 14, 254 and 65534 appear in printout of s. *)
Union[{0, 2}, allS]

PARI

for(n=0,4,if(ispseudoprime(t=2^(2^n)+1),print1(t-3", "))) \\ Charles R Greathouse IV, Apr 26 2012

Formula

a(n) = A019434(n) - 3. [corrected by Jason Yuen, Jun 22 2025]