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A085766
Smallest m such that n divides the tetrahedral number A000292(m+1).
0
1, 1, 6, 1, 2, 6, 4, 5, 24, 2, 8, 6, 10, 5, 7, 13, 14, 25, 16, 3, 6, 9, 20, 7, 22, 10, 78, 5, 26, 7, 28, 29, 8, 14, 4, 25, 34, 17, 24, 7, 38, 6, 40, 9, 24, 21, 44, 15, 46, 22, 15, 11, 50, 78, 8, 5, 16, 26, 56, 7, 58, 29, 25, 61, 12, 42, 64, 14, 43, 13, 68, 53, 70, 34, 24, 17, 19, 25, 76, 13
OFFSET
1,3
EXAMPLE
Let te(m)=(m+1)(m+2)(m+3)/6. Then te(1)=4, te(2)=10, te(3)=20, te(4)=35, te(5)=56 and te(6)=84. te(6) is the first tetrahedral number divisible by 3, hence a(3)=6.
PROG
(PARI) te(n)=(n+1)*(n+2)*(n+3)/6 for (n=1, 50, c=1; while (te(c)%n!=0, c++); print1(c", "))
(PARI) first(n) = {my(res = vector(n), todo = n); res[1] = 1; todo--; for(i = 1, oo, t = binomial(i + 2, 3); d = divisors(t); for(j = 1, #d, if(d[j] <= n && res[d[j]] == 0, res[d[j]] = i - 1; todo--; if(todo <= 0, return(res); ) ) ) ) } \\ David A. Corneth, Mar 22 2021
CROSSREFS
Cf. A011772 (triangular numbers), A019554 (squares).
Sequence in context: A070682 A216415 A112828 * A002329 A053453 A347197
KEYWORD
nonn
AUTHOR
Jon Perry, Jul 22 2003
EXTENSIONS
More terms from David Wasserman, Feb 10 2005
Definition corrected by David A. Corneth, Mar 22 2021
STATUS
approved