A382329 Least positive integer that gives a square of an integer when multiplied by the n-th harmonic number.

1, 6, 66, 12, 8220, 20, 420, 213080, 17965080, 153720, 2320468920, 14109480, 412970037480, 422245703880, 430902992520, 6076390320, 516336630329520, 161488607280, 21362271268818480, 866533600973040, 97555876321904, 186715152624, 52866073370045936

Offset: 1

Author

Ali Sada, Mar 21 2025

Keywords

• nonn

Examples

			6*3/2 = 9, a square of an integer, so a(2) = 6.
		

Links

• M. F. Hasler, Table of n, a(n) for n = 1..150, May 08 2025

Crossrefs

Cf. A001008, A002805, A007913.

Programs

PARI

a(n)={my(s=sum(i=1, n, 1/i)); denominator(s)*core(numerator(s))}; \\ Yifan Xie, Mar 22 2025

PARI

apply( {A382329(n)=denominator(n=harmonic(n))*core(numerator(n))}, [1..20]) \\ M. F. Hasler, May 08 2025

Python

from math import prod
from sympy import harmonic, factorint
def A382329(n):
    a, b = harmonic(n).as_numer_denom()
    return b*prod(p for p, e in factorint(a).items() if e&1) # Chai Wah Wu, Mar 23 2025

Formula

a(n) = A002805(n) * A007913(A001008(n)).

Extensions

More terms from Yifan Xie, Mar 22 2025