A093396 Denominators of n divided by the product of the anti-divisors of n.

2, 3, 6, 2, 30, 15, 4, 42, 42, 10, 270, 54, 8, 33, 2310, 280, 78, 78, 8, 4050, 4050, 14, 1428, 102, 440, 6270, 114, 32, 7938, 257985, 520, 138, 552, 16, 11250, 866250, 616, 1458, 1458, 2720, 14790, 174, 131040, 16926, 17670, 190, 39204, 78408, 8, 2315250

Offset

3,1

Comments

See A066272 for definition of anti-divisor.

Links

Dumitru Damian, Table of n, a(n) for n = 3..10000

Formula

a(n) = A091507(n)/GCD(n, A091507(n))

Example

The anti-divisors of 18 are 4, 5, 7, 12. Hence a(18) = 4*5*7*12/GCD(4*5*7*12, 18) = 280.

Prog

(Python)
import numpy as np
from sympy.ntheory.factor_ import antidivisors
def a093396(k):
        return (m:=np.prod(antidivisors(k), dtype=object))//np.gcd(m, k, dtype=object)
{print(a093396(k), end = ', ') for k in range(3, 10**2)} # Dumitru Damian, Oct 16 2023

Crossrefs

Cf. A066417, A091507, A093394, A093395 (numerators).

Sequence in context: A319432 A115033 A214630 * A189971 A211605 A316610

Adjacent sequences: A093393 A093394 A093395 * A093397 A093398 A093399

Keyword

nonn,frac

Author

Lior Manor, Mar 28 2004

Extensions

Name changed by Franklin T. Adams-Watters, Aug 21 2013

Status

approved