cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A070813 Fermat primes minus 3.

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%I A070813 #28 Jul 12 2025 21:09:41
%S A070813 0,2,14,254,65534
%N A070813 Fermat primes minus 3.
%C A070813 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).
%C A070813 Solutions to A070812(x) = 0 are in A007283, for A070812(x) = 2 are in A070004.
%F A070813 a(n) = A019434(n) - 3. [corrected by _Jason Yuen_, Jun 22 2025]
%t A070813 pf[x_] := Part[Reverse[Flatten[FactorInteger[x]]], 2];
%t A070813 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. *)
%t A070813 Union[{0, 2}, allS]
%o A070813 (PARI) for(n=0,4,if(ispseudoprime(t=2^(2^n)+1),print1(t-3", "))) \\ _Charles R Greathouse IV_, Apr 26 2012
%Y A070813 Cf. A000010, A006530, A019434, A070812, A007283, A070004.
%K A070813 nonn,more
%O A070813 1,2
%A A070813 _Labos Elemer_, May 09 2002