

A286941


Irregular triangle read by rows: the nth row corresponds to the totatives of the nth primorial, A002110(n).


7



1, 1, 5, 1, 7, 11, 13, 17, 19, 23, 29, 1, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 143, 149, 151, 157, 163, 167, 169, 173, 179, 181, 187, 191, 193, 197, 199, 209
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OFFSET

1,3


COMMENTS

Values in row n of a(n) are those of row n of A286942 complement those of row n of A279864.
From Michael De Vlieger, May 18 2017: (Start)
Numbers t < p_n# such that gcd(t, p_n#) = 0, where p_n# = A002110(n).
Numbers in the reduced residue system of A002110(n).
A005867(n) = number of terms of a(n) in row n; local minimum of Euler's totient function.
A048862(n) = number of primes in row n of a(n).
A048863(n) = number of nonprimes in row n of a(n).
Since 1 is coprime to all n, it delimits the rows of a(n).
The prime A000040(n+1) is the second term in row n since it is the smallest prime coprime to A002110(n) by definition of primorial.
The smallest composite in row n is A001248(n+1) = A000040(n+1)^2.
The Kummer numbers A057588(n) = A002110(n)  1 are the last terms of rows n, since (n  1) is less than and coprime to all positive n. (End)


LINKS

Michael De Vlieger, Table of n, a(n) for n = 1..6299 (rows 1 <= n <= 6 flattened).
Mathoverflow, Lower bound for Euler's totient for almost all integers.  Michael De Vlieger, May 18 2017
Eric Weisstein's World of Mathematics, Totative.  Michael De Vlieger, May 18 2017


EXAMPLE

The triangle starts
1;
1, 5;
1, 7, 11, 13, 17, 19, 23, 29;
1, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 143, 149, 151, 157, 163, 167, 169, 173, 179, 181, 187, 191, 193, 197, 199, 209;


MATHEMATICA

Table[Function[P, Select[Range@ P, CoprimeQ[#, P] &]]@ Product[Prime@ i, {i, n}], {n, 4}] // Flatten (* Michael De Vlieger, May 18 2017 *)


PROG

(PARI) row(n) = my(P=factorback(primes(n))); select(x>(gcd(x, P) == 1), [1..P]); \\ Michel Marcus, Jun 02 2020


CROSSREFS

Cf. A002110, A005867, A048862, A057588, A279864, A286941, A286942, A309497, A038110, A058250, A329815.
Cf. A335334 (row sums).
Sequence in context: A342921 A342417 A233091 * A332459 A051854 A006569
Adjacent sequences: A286938 A286939 A286940 * A286942 A286943 A286944


KEYWORD

nonn,tabf


AUTHOR

Jamie Morken and Michael De Vlieger, May 16 2017


EXTENSIONS

More terms from Michael De Vlieger, May 18 2017


STATUS

approved



