A058854 a(n) = largest prime in the factorization of n-th Franel number (A000172).

2, 5, 7, 173, 563, 73, 41, 369581, 1409, 109, 449, 176459, 44221, 12148537, 148381, 11399977, 5779337237, 151431487, 26013917, 57405011, 939783003793, 277157, 191141, 13515438731, 79702499, 236463558839, 1883371283883863, 313527009031, 138961158000728258971

Offset

1,1

Links

Sean A. Irvine, Table of n, a(n) for n = 1..150

Example

a(4)=173 because the 4th Franel number is 346 = 2^1 * 173^1, in which 173 is the largest prime.

Maple

with(combinat): with(numtheory): A000172 := n->sum(binomial(n, k)^3, k=0..n): for n from 1 to 50 do printf(`%d, `, sort(ifactors(A000172(n))[2])[nops(ifactors(A000172(n))[2])][1]) od: # Corrected by Sean A. Irvine, Aug 31 2022
# second Maple program:
a:= n-> max(numtheory[factorset](add(binomial(n, k)^3, k=0..n))):
seq(a(n), n=1..30);  # Alois P. Heinz, Aug 31 2022

Mathematica

Do[ Print[ FactorInteger[ Sum[ Binomial[n, k]^3, {k, 0, n}]] [[ -1, 1]] ], {n, 1, 32} ]

Crossrefs

Cf. A000172.

Sequence in context: A265815 A041961 A242169 * A006275 A042673 A214705

Adjacent sequences: A058851 A058852 A058853 * A058855 A058856 A058857

Keyword

nonn

Author

Felix Goldberg (felixg(AT)tx.technion.ac.il), Jan 30 2001

Extensions

More terms from James A. Sellers, Feb 01 2001

Data corrected and entry revised by Sean A. Irvine, Aug 31 2022

Status

approved