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A058854
a(n) = largest prime in the factorization of n-th Franel number (A000172).
1
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
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
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