A285183 Nearest integer to n*omega(n)/phi(n).

0, 2, 2, 2, 1, 6, 1, 2, 2, 5, 1, 6, 1, 5, 4, 2, 1, 6, 1, 5, 4, 4, 1, 6, 1, 4, 2, 5, 1, 11, 1, 2, 3, 4, 3, 6, 1, 4, 3, 5, 1, 11, 1, 4, 4, 4, 1, 6, 1, 5, 3, 4, 1, 6, 3, 5, 3, 4, 1, 11, 1, 4, 4, 2, 3, 10, 1, 4, 3, 9, 1, 6, 1, 4, 4, 4, 3, 10, 1, 5, 2, 4, 1, 11, 3, 4, 3, 4, 1, 11, 3, 4, 3, 4, 3, 6

Offset: 1

Author

N. J. A. Sloane, Apr 19 2017

Keywords

• nonn

Comments

n*omega(n)/phi(n) appears in certain bounds of Erdős for the Jacobsthal function g(n) (A048669).

References

• József Sándor, Dragoslav S. Mitrinovic, and Borislav Crstici, Handbook of Number Theory I, Springer Science & Business Media, 2005, Chapter I, p. 34, section I.32.3.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• Paul Erdős, On the integers relatively prime to n and on a number theoretic function considered by Jacobsthal, Math. Scand., 10, 1962, 163-170.

Crossrefs

Cf. A000010 (phi), A001221 (omega), A048669.

Programs

Magma

[Round(n*#PrimeDivisors(n)/EulerPhi(n)): n in [1..100]]; // Vincenzo Librandi, Apr 21 2017

Maple

Digits:=30;
A001221 := proc(n) nops(numtheory[factorset](n)) end proc:
with(numtheory);
f:=n->round(n*A001221(n)/phi(n));
t1:=[seq(f(n),n=1..130)];

Mathematica

Round[Table[(n PrimeNu[n] + 1/2)/EulerPhi[n], {n, 1, 100}]] (* Vincenzo Librandi, Apr 21 2017 - confirmed by Giovanni Resta *)

PARI

a(n) = {my(f = factor(n)); round(n*omega(f)/eulerphi(f));} \\ Amiram Eldar, Apr 25 2024