A382213 Largest squarefree number dividing the numerator of harmonic number H(n).
1, 3, 11, 5, 137, 7, 33, 761, 7129, 671, 83711, 6617, 1145993, 1171733, 1195757, 143327, 42142223, 751279, 275295799, 55835135, 18858053, 830139, 444316699, 1347822955, 34052522467, 34395742267, 312536252003, 10876020307, 214582477009, 300151059037, 290774257297357
Offset: 1
Keywords
Examples
A001008(4) = 25, and the largest squarefree divisor of 25 is 5, so a(4) = 5.
Programs
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Maple
a:= n-> mul(i[1], i=ifactors(numer(harmonic(n)))[2]): seq(a(n), n=1..35); # Alois P. Heinz, Apr 23 2025
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PARI
a(n) = factorback(factor(numerator(sum(k=1, n, 1/k)))[, 1]); \\ Michel Marcus, Apr 24 2025