A081395 -id:A081395 - cp's OEIS frontend

A081393 a(n) is the smallest k such that number of non-unitary prime divisors of central binomial coefficient, A000984(k) = C(2*k,k) equals n.

1, 3, 5, 14, 48, 74, 182, 314, 480, 774, 960, 1321, 1323, 1670, 3121, 3455, 3457, 3472, 3462, 3469, 8203, 9991, 12163, 15838, 15840, 17665, 18480, 18482, 19458, 19464, 36782, 19865, 36789, 40048, 43603, 43655, 47518, 61654, 61653, 61685, 61684, 87120, 92958, 93181, 93185, 93187, 93191

Offset: 0

Labos Elemer, Mar 27 2003

nonn

			n=5: a(5)=74, C(148,74) has 5 non-unitary prime divisors: {2,3,5,7,11} and 74 is the smallest.

Cf. A081387, A081394, A081395.

seq[len_, kmax_] := Module[{s = Table[0, {len}], k = 1, c = 0, i}, While[c < len && k < kmax, i = Count[FactorInteger[Binomial[2*k, k]][[;; , 2]], ?(# > 1 &)] + 1; If[i <= len && s[[i]] == 0, c++; s[[i]] = k]; k++]; TakeWhile[s, # > 0 &]]; seq[20, 10^4] (* _Amiram Eldar, May 15 2023 *)

a(n) = Min{k; A081387(k) = n}.

a(11)-a(21) from Michel Marcus, Sep 01 2019

a(22)-a(46) from Amiram Eldar, May 15 2023

A081394 a(n) is the smallest k such that number of non-unitary prime divisors of central binomial coefficient, A001405(k) = C(k, floor(k/2)) equals n.

Original entry on oeis.org

1, 6, 10, 27, 96, 147, 363, 627, 959, 1547, 1919, 2641, 2645, 3339, 6241, 6909, 6913, 6943, 6923, 6937, 16405, 19981, 24325, 31675, 31679, 35329, 36959, 36963, 38915, 38927, 73563, 39729, 73577, 80095, 87205, 87309, 95035, 123307, 123305, 123369, 123367, 174239, 185915, 186361, 186369, 186373, 186381

Offset: 0

Labos Elemer, Mar 27 2003

nonn

			n=8: a(8)=959, C(959,479) has 8 non-unitary prime divisors: {2,3,5,7,11,13,23,29} and 959 is the smallest.

Cf. A081387, A081393, A081395, A056175.

seq[len_, kmax_] := Module[{s = Table[0, {len}], k = 1, c = 0, i}, While[c < len && k < kmax, i = Count[FactorInteger[Binomial[k, Floor[k/2]]][[;; , 2]], ?(# > 1 &)] + 1; If[i <= len && s[[i]] == 0, c++; s[[i]] = k]; k++]; TakeWhile[s, # > 0 &]]; seq[20, 10^4] (* _Amiram Eldar, May 15 2023 *)

a(n) = Min{k; A056175(k) = n}.

a(9)-a(19) from Michel Marcus, Sep 01 2019

a(20)-a(46) from Amiram Eldar, May 15 2023

cp's OEIS Frontend

A081393 a(n) is the smallest k such that number of non-unitary prime divisors of central binomial coefficient, A000984(k) = C(2*k,k) equals n.

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