A249670 a(n) = A017665(n)*A017666(n).

1, 6, 12, 28, 30, 2, 56, 120, 117, 45, 132, 21, 182, 84, 40, 496, 306, 78, 380, 210, 672, 198, 552, 10, 775, 273, 1080, 2, 870, 60, 992, 2016, 176, 459, 1680, 3276, 1406, 570, 2184, 36, 1722, 112, 1892, 231, 390, 828, 2256, 372, 2793, 4650, 408, 1274, 2862

Offset: 1

Author

Michel Marcus, Nov 03 2014

Keywords

• nonn

Comments

If n is a k-multiperfect, then a(n) = k.

Links

• Allan C. Wechsler, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000203 (sigma(n)).

Cf. A017665/A017666 (abundancy of n).

Cf. A009194 (gcd(n, sigma(n))), A064987 (n*sigma(n)).

Cf. A000396, A005820, A027687, A046060, A046061.

Programs

Haskell

a249670 n = div (n * s) (gcd n s ^ 2)
 where s = sum (filter (\k -> mod n k == 0) [1..n])
-- Allan C. Wechsler, Mar 31 2023

Mathematica

a249670[n_Integer] := Numerator[DivisorSigma[-1, n]]*Denominator[DivisorSigma[-1, n]]; a249670 /@ Range[80] (* Michael De Vlieger, Nov 10 2014 *)

PARI

a(n) = my(ab = sigma(n)/n); numerator(ab)*denominator(ab);

Formula

a(n) = A064987(n)/A009194(n)^2.

a(A000396(n)) = 2 (perfect).

a(A005820(n)) = 3 (tri-perfect).

For p prime, a(p) = p*(p+1).