A239363 Numbers k such that phi(k+1) - phi(k) = k/2.

2, 4, 16, 24, 216, 256, 4960, 10648, 65536, 195112, 1191016, 7544800, 11530464, 12705504, 45882712, 55742968, 179883264, 946966168, 2106997768, 2289529432, 2548895896, 3056745600, 3482123272, 7756683264, 10735357816, 15920801280, 26946035992, 46827274240

Offset: 1

Author

Paolo P. Lava, Mar 17 2014

Keywords

• nonn

Comments

From Amiram Eldar, Nov 09 2024: (Start)

If p is a Fermat prime (A019434), then p-1 is a term.

If p is a term of A237038, then 8*p^3 is a term. (End)

Examples

			phi(217) = 180, phi(216) = 72, and 180-72 = 108, which is 216/2.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..39 (terms < 10^12)

Crossrefs

Cf. A000010, A019434, A237038.

Programs

Maple

with(numtheory); P:=proc(q) local n;
for n from 1 to q do if phi(n+1)-phi(n)=n/2 then print(n);
fi; od; end: P(10^9);

Mathematica

Select[Range[200000], EulerPhi[#+1] - EulerPhi[#] == #/2 &] (* Amiram Eldar, Nov 09 2024 *)

PARI

is(k) = eulerphi(k+1) - eulerphi(k) == k/2; \\ Amiram Eldar, Nov 09 2024

Extensions

a(13)-a(27) from Giovanni Resta, Mar 17 2014