A125704 Table read by antidiagonals: row n contains the positive integers (in order) which are coprime to the n-th prime.
1, 1, 3, 1, 2, 5, 1, 2, 4, 7, 1, 2, 3, 5, 9, 1, 2, 3, 4, 7, 11, 1, 2, 3, 4, 6, 8, 13, 1, 2, 3, 4, 5, 7, 10, 15, 1, 2, 3, 4, 5, 6, 8, 11, 17, 1, 2, 3, 4, 5, 6, 8, 9, 13, 19, 1, 2, 3, 4, 5, 6, 7, 9, 11, 14, 21, 1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 16, 23, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 17, 25, 1, 2, 3, 4, 5
Offset: 1
Examples
Beginning of table: 1, 3, 5, 7, 9, 11, 13, ... 1, 2, 4, 5, 7, 8, 10, 11, ... 1, 2, 3, 4, 6, 7, 8, 9, 11, ... 1, 2, 3, 4, 5, 6, 8, 9, 10, ...
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..11325 (rows 1 <= n <= 150).
Programs
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Maple
A125704 := proc(n,m) local p,i,a ; p := ithprime(n) ; a := 1 ; for i from 2 to m do a := a+1 ; while gcd(a,p) <> 1 do a := a+1 ; od ; od ; RETURN(a) ; end : maxdiag := 15 ; for d from 1 to maxdiag do for n from d to 1 by -1 do printf("%d,",A125704(n,d-n+1)) ; od ; od; # R. J. Mathar, Feb 02 2007
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Mathematica
Table[Function[n, k - 1 + Floor[(k + Prime[n] - 2)/(Prime[n] - 1)]][m - k + 1], {m, 14}, {k, m}] // Flatten (* Michael De Vlieger, Oct 10 2017, after PARI by Benoit Cloitre *) -
PARI
T(n,m)=m-1+floor((m+prime(n)-2)/(prime(n)-1)) \\ Benoit Cloitre, Jul 11 2009
Formula
T(1,m) = A005408(m). T(2,m) = A001651(m). T(3,m) = A047201(m). T(4,m) = A047304(m). - R. J. Mathar, Feb 02 2007
T(n,m) = m - 1 + floor((m+prime(n)-2)/(prime(n)-1)) where prime(n) = n-th prime. - Benoit Cloitre, Jul 11 2009
Extensions
More terms from R. J. Mathar, Feb 02 2007