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A242174 Least prime divisor of A005260(n) which does not divide any previous term A005260(k) with k < n, or 1 if such a primitive prime divisor of A005260(n) does not exist. 4
2, 3, 41, 5, 7, 349, 61, 75617, 31, 13, 499, 643897693, 17, 19, 1729774061, 101, 2859112064587, 138407, 83, 167, 59, 29, 653, 257, 997540809461453561581, 347, 13679, 37, 160449179727717672892660463, 211, 151, 43, 97, 73, 47 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecture: a(n) is prime for any n > 0. In general, for any r > 2, if n is large enough then f_r(n) = sum_{k=0..n}C(n,k)^r has a prime divisor which does not divide any previous terms f_r(k) with k < n.

LINKS

Zhi-Wei Sun, Table of n, a(n) for n = 1..82

EXAMPLE

a(3) = 41 since A005260(3) = 2^2*41 with 41 dividing none of A005260(1) = 2 and A005260(2) = 2*3^2.

MATHEMATICA

u[n_]:=Sum[Binomial[n, k]^4, {k, 0, n}]

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

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

Do[If[u[n]<2, Goto[cc]]; Do[Do[If[Mod[u[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, 35}]

CROSSREFS

Cf. A000040, A005260, A242169, A242170, A242171, A242173, A242193, A242194, A242195, A242207.

Sequence in context: A157132 A262189 A077336 * A288519 A240588 A013646

Adjacent sequences:  A242171 A242172 A242173 * A242175 A242176 A242177

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, May 07 2014

STATUS

approved

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Last modified December 5 15:11 EST 2019. Contains 329753 sequences. (Running on oeis4.)