A083533 First difference sequence of A002202. Difference between consecutive possible values of phi(n), the Euler totient function A000010.

1, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 4, 2, 2, 4, 4, 2, 2, 2, 2, 4, 2, 2, 2, 2, 4, 2, 4, 2, 6, 2, 2, 2, 4, 4, 4, 4, 2, 2, 2, 2, 2, 2, 4, 4, 6, 2, 2, 2, 4, 2, 2, 4, 4, 2, 6, 4, 2, 2, 2, 2, 4, 4, 2, 2, 4, 6, 2, 4, 2, 2, 4, 4, 2, 2, 4, 4, 2, 2, 2, 2, 4, 6, 2, 10, 2, 4, 4, 2, 2, 4, 2, 2, 4, 4, 2, 6, 4, 2, 2, 4, 6, 4, 2, 4

Offset: 1

Author

Labos Elemer, May 20 2003

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000010, A002202, A005277, A083531, A083532, A083534, A083535, A083536.

Programs

Haskell

a083533 n = a083533_list !! (n-1)
a083533_list = zipWith (-) (tail a002202_list) a002202_list
-- Reinhard Zumkeller, Nov 26 2015

Mathematica

t=Table[EulerPhi[w], {w, 1, 25000}]; u=Union[%]; Delete[u-RotateRight[u], 1]

PARI

lista(lim) = {my(k1 = 1, k2 = 1); while(k1 < lim, until(istotient(k2), k2++); print1(k2 - k1, ", "); k1 = k2);} \\ Amiram Eldar, Nov 16 2024

Formula

a(n) = A002202(n+1) - A002202(n).