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A242173 Least prime divisor of the n-th central Delannoy number D(n) which does not divide any D(k) with k < n, or 1 if such a primitive prime divisor of D(n) does not exist. 11
3, 13, 7, 107, 11, 89, 31, 265729, 19, 9887, 23, 113, 79, 373, 53, 3089, 151, 127, 719, 193, 43, 482673878761, 47, 61403, 109, 37889, 1223, 3251609, 59, 181, 22504880485262968151, 3598831, 67, 69593, 179, 13828116559, 4247285503, 1579, 19095283759, 619 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecture:

(i) a(n) > 1 for all n > 0.

(ii) For any integer n > 0, the n-th Apéry number A(n) = Sum_{k=0..n} (binomial(n,k)*binomial(n+k,k))^2 has a prime divisor which does not divide any A(k) with k < n.

LINKS

Zhi-Wei Sun, Table of n, a(n) for n = 1..119

EXAMPLE

a(3) = 7 since D(3) = 3^2*7 with 7 dividing none of D(1) = 3 and D(2) = 13.

MATHEMATICA

d[n_]:=Sum[Binomial[n+k, k]*Binomial[n, k], {k, 0, n}]

f[n_]:=FactorInteger[d[n]]

p[n_]:=Table[Part[Part[f[n], k], 1], {k, 1, Length[f[n]]}]

Do[If[d[n]<2, Goto[cc]]; Do[Do[If[Mod[d[i], Part[p[n], k]]==0, Goto[aa]], {i, 1, n-1}]; Print[n, " ", Part[p[n], k]]; Goto[bb]; Label[aa]; Continue, {k, 1, Length[p[n]]}]; Label[cc]; Print[n, " ", 1]; Label[bb]; Continue, {n, 1, 40}]

CROSSREFS

Cf. A000040, A001850, A005259, A242169, A242170, A242171.

Sequence in context: A173203 A140445 A320039 * A186109 A012789 A273025

Adjacent sequences:  A242170 A242171 A242172 * A242174 A242175 A242176

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, May 06 2014

STATUS

approved

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Last modified December 11 18:19 EST 2019. Contains 329925 sequences. (Running on oeis4.)