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

Author

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

Keywords

• nonn

Examples

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

Links

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

Crossrefs

Cf. A000172.

Programs

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} ]

Extensions

More terms from James Sellers, Feb 01 2001

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