A358309 a(n) = floor(n*sqrt(gamma(n))) - sigma(n), where sigma(n) = A000203(n) is the sum of the divisors of n and gamma(n) = A007947(n) is the greatest squarefree divisor of n.

0, -1, 1, -2, 5, 2, 10, -4, 2, 13, 24, 1, 32, 28, 34, -9, 52, 5, 62, 21, 64, 67, 86, -2, 24, 90, 6, 48, 126, 92, 140, -18, 141, 144, 159, -3, 187, 174, 187, 36, 220, 176, 237, 122, 96, 239, 274, -7, 72, 65, 292, 167, 331, 12, 335, 89, 350, 351, 393, 160, 414, 392, 184, -37, 440, 392, 480, 270, 477, 441, 526

Offset

1,4

Comments

It appears that almost always sigma(n) <= n*sqrt(gamma(n)) (see A358308).

References

D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, page 77, Section III.1.1.d.

Links

Table of n, a(n) for n=1..71.

Crossrefs

Cf. A000203, A007947, A358308.

Sequence in context: A178310 A210697 A085020 * A276609 A292591 A240760

Adjacent sequences: A358306 A358307 A358308 * A358310 A358311 A358312

Keyword

sign

Author

N. J. A. Sloane, Dec 09 2022

Status

approved