A079814 Odd integers such that phi(n)/n < 6/Pi^2 where phi = A000010.

15, 21, 33, 45, 63, 75, 99, 105, 135, 147, 165, 189, 195, 225, 231, 255, 273, 285, 297, 315, 345, 357, 363, 375, 399, 405, 429, 435, 441, 465, 483, 495, 525, 555, 561, 567, 585, 609, 615, 627, 645, 651, 663, 675, 693, 705, 735, 741, 759, 765, 777, 795, 819

Offset

1,1

Comments

Since, as Euler proved, the random chance of two integers not having a common prime factor is 6/Pi^2, these are the odd integers that share common factors with an above average fraction of integers. Is it known, or can it be calculated, what portion of odd integers satisfy this condition? (All even numbers qualify; for all multiples of 2, phi(n)/n <= 0.5.)

The sequence is closed under multiplication by any odd number. If we include the even numbers, the sequence of primitive terms begins 2, 15, 21, 33, 663, ... . - Peter Munn, Apr 11 2021

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

phi(33)/33 = 20/33 or 0.6060606...; 6/Pi^2 is 0.6079271....

Prog

(PARI) is(n)=n%2 && eulerphi(n)/n<6/Pi^2 \\ Charles R Greathouse IV, Sep 13 2013

Crossrefs

Cf. A000010 (Euler totient function phi(n)), A280877, A280878, A280879.

Sequence in context: A127329 A043326 A179996 * A168354 A190358 A090999

Adjacent sequences: A079811 A079812 A079813 * A079815 A079816 A079817

Keyword

easy,nonn

Author

Matthew Vandermast, Feb 19 2003

Status

approved