

A064379


Triangle whose nth row is list of numbers that are infinitarily relatively prime to n (n=2,3,..).


2



1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 4, 5, 1, 2, 3, 4, 5, 6, 1, 3, 5, 7, 1, 2, 3, 4, 5, 6, 7, 8, 1, 3, 4, 7, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 5, 7, 9, 10, 11, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 3, 4, 5, 9, 11, 12, 13, 1, 2, 4, 7, 8, 9, 11, 13, 14, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14
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OFFSET

2,3


COMMENTS

The integers less than n that have no common infinitary divisors with n.


LINKS

Table of n, a(n) for n=2..97.
Eric Weisstein, Infinitary Divisor


EXAMPLE

irelprime[6]={1, 4, 5} because iDivisors[6]={1, 2, 3, 6} and iDivisors[4]={1, 4} so 4 is infinitary_relatively_prime to 6 since it lacks common infinitary divisors with 6.
For n = 2 ..8 irelprime[n] gives {1}, {1,2}, {1,2,3}, {1,2,3,4}, {1,4,5}, {1,2,3,4,5,6}, {1,3,5,7}
Triangle starts:
02: 1,
03: 1, 2,
04: 1, 2, 3,
05: 1, 2, 3, 4,
06: 1, 4, 5,
07: 1, 2, 3, 4, 5, 6,
08: 1, 3, 5, 7,
09: 1, 2, 3, 4, 5, 6, 7, 8,
10: 1, 3, 4, 7, 9,
11: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,
12: 1, 2, 5, 7, 9, 10, 11,
13: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,
14: 1, 3, 4, 5, 9, 11, 12, 13,
15: 1, 2, 4, 7, 8, 9, 11, 13, 14,


MATHEMATICA

irelprime[ n_ ] := Select[ temp=iDivisors[ n ]; Range[ n ], Intersection[ iDivisors[ # ], temp ]==={1}& ]; (* with iDivisors of n as *) bitty[ k_ ] := Union[ Flatten[ Outer[ Plus, Sequence@@{0, #1}&/@Union[ 2^Range[ 0, Floor[ Log[ 2, k ] ] ]*Reverse[ IntegerDigits[ k, 2 ] ] ] ] ] ]; iDivisors[ k_Integer ] := Sort[ (Times @@(First[ it ]^(#1/.z> List))&)/@Flatten[ Outer[ z, Sequence@@bitty/@Last[ it=Transpose[ FactorInteger[ k ] ] ], 1 ] ] ]; iDivisors[ 1 ] := {1};


CROSSREFS

Cf. A037445, A064380.
Sequence in context: A318806 A066019 A051237 * A278961 A194973 A195113
Adjacent sequences: A064376 A064377 A064378 * A064380 A064381 A064382


KEYWORD

nonn,tabf


AUTHOR

Wouter Meeussen, Sep 27 2001


STATUS

approved



