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A133927
Numbers k such that the sum of the first k Catalan numbers, C_1 + C_2 + ... + C_k, is divisible by k.
0
1, 30, 494, 6331, 36851, 95450, 122614, 940745, 5126032, 7519204
OFFSET
1,2
COMMENTS
The sum of the first 30 Catalan numbers, 1 + 2 + 5 + ... + 3814986502092304 = 5175497420902740, is divisible by 30, so 30 is a term.
No more terms < 5*10^7. - Lars Blomberg, Nov 07 2011
LINKS
Eric Weisstein's World of Mathematics, Catalan Number
MATHEMATICA
Module[{nn=40000, lst}, lst=Thread[{Range[nn], Accumulate[CatalanNumber[Range[nn]]]}]; Position[ lst, _?(Mod[#[[2]], #[[1]]]==0&), 1, Heads->False]]//Flatten (* The program generates the first 5 terms of the sequence. *) (* Harvey P. Dale, Jun 18 2024 *)
CROSSREFS
Sequence in context: A258417 A212473 A127544 * A082556 A036223 A022658
KEYWORD
hard,more,nonn
AUTHOR
Ryan Propper, Jan 07 2008
STATUS
approved