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A248133
Least positive integer m such that m + n divides T(m) + T(n), where T(.) is given by A002426.
6
1, 3, 1, 1, 7, 2, 2, 2, 1, 1, 7, 4, 37, 145, 35, 1, 25, 16, 5, 16, 1, 1, 18, 19, 3, 11, 41, 1, 7, 2, 48, 415, 1, 2, 15, 7, 13, 34, 97, 1, 27, 18, 56, 22, 1, 1, 5, 26, 22, 36, 18, 1, 117, 52, 376, 11, 1, 1, 23, 26
OFFSET
1,2
COMMENTS
Conjecture: a(n) exists for any n > 0. Moreover, a(n) <= n^2 - n + 1 except for n = 274.
Note that a(274) = 188847 > 2*274^2.
EXAMPLE
a(5) = 7 since 5 + 7 divides T(5) + T(7) = 51 + 393 = 444 = 12*37.
a(2539) = 643425 since 2539 + 643425 = 645964 divides T(2539) + T(643425).
MATHEMATICA
T[n_]:=Sum[Binomial[n, 2k]Binomial[2k, k], {k, 0, n/2}]
Do[m=1; Label[aa]; If[Mod[T[m]+T[n], m+n]==0, Print[n, " ", m]; Goto[bb]]; m=m+1; Goto[aa]; Label[bb]; Continue, {n, 1, 60}]
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Oct 02 2014
STATUS
approved