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A248137
Least positive integer m such that m + n divides M(m) + M(n), where M(.) is given by A001006.
6
1, 1, 244, 1, 23, 4, 1, 1, 3494, 1, 68058, 4, 20, 18, 35, 1, 4, 14, 32, 13, 21, 1, 5, 22, 172, 7, 8, 1, 1, 28, 14, 19, 2, 178, 15, 227, 2, 6, 109, 1, 22, 122, 47, 22, 126, 1, 43, 60, 41, 18, 24, 1, 13, 23, 21, 24, 126, 1, 152, 6
OFFSET
1,3
COMMENTS
Conjecture: a(n) exists for any n > 0.
EXAMPLE
a(5) = 23 since 5 + 23 = 28 divides M(5) + M(23) = 21 + 1129760415 = 1129760436 = 28*40348587.
MATHEMATICA
M[n_]:=Sum[Binomial[n, 2k]Binomial[2k, k]/(k+1), {k, 0, n/2}]
Do[m=1; Label[aa]; If[Mod[M[m]+M[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