A075626 a(1) = 1, then group the natural numbers so that the n-th group contains n numbers relatively prime to n whose sum is divisible by n.

1, 3, 5, 2, 8, 11, 7, 9, 13, 15, 4, 6, 12, 14, 19, 17, 23, 25, 29, 31, 37, 10, 16, 18, 20, 22, 24, 30, 21, 27, 33, 35, 39, 41, 43, 49, 26, 28, 32, 34, 38, 40, 44, 47, 53, 51, 57, 59, 61, 63, 67, 69, 71, 73, 79, 36, 42, 45, 46, 48, 50, 52, 54, 56, 58, 74, 55, 65, 77, 83, 85, 89

Offset

1,2

Links

Table of n, a(n) for n=1..72.

Example

Triangle begins:
   1;
   3,  5;
   2,  8, 11;
   7,  9, 13, 15;
   4,  6, 12, 14, 19;
  17, 23, 25, 29, 31, 37;
  ...
T(3, 2) is 8 because if it were 4 or 7, we could not add a number relatively prime to 3 and get a sum divisible by 3.

Prog

(PARI) print1(1, " "); used = vector(10000); used[1] = 1; x = 2; for (n = 2, 15, i = x; s = 0; for (k = 1, n - 2, while (used[i] || gcd(i, n) > 1, i++); print1(i, " "); used[i] = 1; s += i; i++); while (used[i] || gcd(i, n) > 1 || gcd(i + s, n) > 1, i++); print1(i, " "); used[i] = 1; s += i; i += (n - (i + s)%n); while (used[i], i += n); print1(i, " "); used[i] = 1; while (used[x], x++)); \\ David Wasserman, Jan 22 2005

Crossrefs

Cf. A075627, A075628, A075629, A075630.

Sequence in context: A026193 A026143 A340510 * A152649 A327263 A186412

Adjacent sequences: A075623 A075624 A075625 * A075627 A075628 A075629

Keyword

nonn,tabl

Author

Amarnath Murthy, Sep 30 2002

Extensions

More terms from David Wasserman, Jan 22 2005

Status

approved