A152982 -id:A152982 - cp's OEIS frontend

A153787 Largest proper divisor of Motzkin number A001006(n).

1, 2, 3, 7, 17, 1, 19, 167, 1094, 2899, 1, 13945, 56817, 155286, 284489, 785593, 3268191, 9099642, 16950673, 47515853, 133587741, 376586805, 1064242599, 1291914643, 12834909238, 36503886401, 1944142787, 19152993059, 1144562017

Offset: 2

Omar E. Pol, Jan 16 2009

nonn

Amiram Eldar, Table of n, a(n) for n = 2..200

Cf. A001006, A032742, A152766, A152982.

with(numtheory): M := proc (n) options operator, arrow: (sum((-1)^j*binomial(n+1, j)*binomial(2*n-3*j, n), j = 0 .. floor((1/3)*n)))/(n+1) end proc: seq(divisors(M(i))[tau(M(i))-1], i = 2 .. 32); # Emeric Deutsch, Jan 18 2009

mot[0] = 1; mot[n_] := mot[n] = mot[n - 1] + Sum[mot[k] * mot[n - 2 - k], {k, 0, n - 2}]; lpd[n_] := n / FactorInteger[n][[1, 1]]; Table[lpd[mot[n]], {n, 2, 30}] (* Amiram Eldar, Nov 26 2019 *)

Extended by Emeric Deutsch, Jan 18 2009

a(23)-a(27) and a(29)-a(30) corrected by Amiram Eldar, Nov 26 2019

A154349 Sum of proper divisors minus the number of proper divisors of Motzkin number A001006(n).

Original entry on oeis.org

0, 0, 0, 1, 2, 8, 18, 0, 34, 170, 1643, 3603, 0, 25118, 139063, 474559, 284490, 984006, 6536387, 24265729, 18678366, 96214018, 277799290, 1282283434, 2077807072, 1899874612, 19252363859, 44221482383, 1967547352, 29743945396, 1265868622

Offset: 0

Omar E. Pol, Jan 07 2009

nonn

Note that, if a(n) != 0 then Motzkin number A001006(n) is a composite number (A002808), otherwise A001006(n) is a noncomposite number (A008578). See A152770.

Amiram Eldar, Table of n, a(n) for n = 0..201

Cf. A001006, A001065, A002808, A032741, A008578, A152770, A152981, A152982, A152983, A152988, A152990.

with(numtheory): M := proc (n) options operator, arrow: (sum((-1)^j*binomial(n+1, j)*binomial(2*n-3*j, n), j = 0 .. floor((1/3)*n)))/(n+1) end proc: seq(sigma(M(n))-M(n)-tau(M(n))+1, n = 0 .. 30); # Emeric Deutsch, Jan 12 2009

mot[0] = 1; mot[n_] := mot[n] = mot[n - 1] + Sum[mot[k] * mot[n - 2 - k], {k, 0, n - 2}]; diff[n_] := DivisorSigma[1, n] - DivisorSigma[0, n] - n + 1; Table[diff[mot[n]], {n, 0, 30}] (* Amiram Eldar, Nov 26 2019 *)

a(n) = A001065(A001006(n)) - A032741(A001006(n)) = A152770(A001006(n)).

Extended by Emeric Deutsch, Jan 12 2009

cp's OEIS Frontend

A153787 Largest proper divisor of Motzkin number A001006(n).

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