A062356 a(n) = floor(n/phi(n)).

1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 1, 2, 1, 3, 1, 2, 2

Offset: 1

Author

Jason Earls, Jul 07 2001

Keywords

• easy
• nonn

Comments

Reference does not include the floor function.

See A007694 for the numbers for which n/phi(n) is an integer, and A049237 for the ratios.

References

• D. M. Burton, Elementary Number Theory, Allyn and Bacon Inc. Boston MA, 1976, Prob. 7-4 3, p. 152.

Links

• Harry J. Smith, Table of n, a(n) for n=1,...,2000

Crossrefs

Cf. A000010, A007694, A049237.

Programs

Mathematica

Table[Floor[n/EulerPhi@ n], {n, 120}] (* Michael De Vlieger, Jul 02 2016 *)

PARI

(a(n)=n\eulerphi(n)); vector(250,n,a(n)) \\ Edited by M. F. Hasler, Jul 02 2016

PARI

{ for (n=1, 2000, write("b062356.txt", n, " ", floor(n/eulerphi(n))) ) } \\ Harry J. Smith, Aug 05 2009; irrelevant realprecision(...) deleted by M. F. Hasler, Jul 02 2016

Formula

From M. F. Hasler, Jul 02 2016: (Start)

A062356(n = 2k+1) = 1 except for n in A036798.

A062356(n = 6k+2) = 2 except for n in 70*{11, 17, 23, 26, 29, 38, 44, 62, 65, 68, 77, 92, 95, 104, 110, ...} or n in 10*{2717, 4199, 4301, 4433, 4862, 5291, 5423, 6149, 6578, 7106, 8294, 8723, 9581, 9614, ...} or n = 646646, 874874, ....

A062356(n = 6k+4) = 2 except for n in 70*{13, 19, 22, 31, 34, 46, 52, 55, 58, 76, 85, 88, 91, 115, 121, ...} or n in 10*{2431, 3289, 3553, 4147, 4807, 5083, 5434, 5797, 5863, 6061, 6721, 6919, 7579, 8398, 8437, 8602, 8866, 9724, ...} or n = 782782, 986986, ....

A062356(n = 6k) = 3 except for n in 30*{7, 11, 13, 14, 21, 22, 26, 28, 33, 35, 39, 42, 44, 49, 52, 55, 56, 63, 65, 66, 70, 77, 78, 84, 88, 91, 98, 99, ...} or n in 42*{143, 187, 209, 221, 247, 253, 286, 374, 418, 429, 442, 494, 506, 561, 572, 627, 663, 741, 748, 759, 836, 858, 884,...} or n = 277134, 554268, 831402, .... (End)