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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.
4
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
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
KEYWORD
nonn,tabl
AUTHOR
Amarnath Murthy, Sep 30 2002
EXTENSIONS
More terms from David Wasserman, Jan 22 2005
STATUS
approved