A242180 Least prime divisor of q(n) which does not divide any q(k) with k < n, or 1 if such a primitive prime divisor does not exist, where q(.) is the strict partition function given by A000009.

1, 1, 2, 1, 3, 1, 5, 1, 1, 1, 1, 1, 1, 11, 1, 1, 19, 23, 1, 1, 1, 89, 13, 61, 71, 1, 1, 37, 1, 1, 17, 1, 7, 1, 1, 167, 1, 1, 491, 53, 1, 31, 1, 227, 1, 1, 1, 97, 1, 59, 241, 29, 1, 953, 1063, 1777, 1, 367, 1, 1

Offset

1,3

Comments

Conjecture: a(n) > 1 for all n > 203.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..6000

Example

a(8) = 1 since q(8) = 2*3 with 2 = q(3) and 3 = q(5).
a(23) = 13 since q(23) = 2^3*13 with 13 not dividing q(1)*q(2)*...*q(22), but 2 divides q(3) = 2.

Mathematica

f[n_]:=FactorInteger[PartitionsQ[n]]
pp[n_]:=Table[Part[Part[f[n], k], 1], {k, 1, Length[f[n]]}]
Do[If[PartitionsQ[n]<2, Goto[cc]]; Do[Do[If[Mod[PartitionsQ[i], Part[pp[n], k]]==0, Goto[aa]], {i, 1, n-1}]; Print[n, " ", Part[pp[n], k]]; Goto[bb]; Label[aa]; Continue, {k, 1, Length[pp[n]]}]; Label[cc]; Print[n, " ", 1]; Label[bb]; Continue, {n, 1, 60}]

Crossrefs

Cf. A000009, A000040, A084911, A194261, A272170, A272171, A272173.

Sequence in context: A295785 A069230 A349348 * A163961 A354366 A101387

Adjacent sequences: A242177 A242178 A242179 * A242181 A242182 A242183

Keyword

nonn

Author

Zhi-Wei Sun, May 06 2014

Status

approved