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A249670
a(n) = A017665(n)*A017666(n).
6
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
1,2
COMMENTS
If n is a k-multiperfect, then a(n) = k.
LINKS
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).
MATHEMATICA
a249670[n_Integer] := Numerator[DivisorSigma[-1, n]]*Denominator[DivisorSigma[-1, n]]; a249670 /@ Range[80] (* Michael De Vlieger, Nov 10 2014 *)
PROG
(PARI) a(n) = my(ab = sigma(n)/n); numerator(ab)*denominator(ab);
(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
CROSSREFS
Cf. A000203 (sigma(n)).
Cf. A017665/A017666 (abundancy of n).
Cf. A009194 (gcd(n, sigma(n)), A064987(n*sigma(n)).
Sequence in context: A030775 A057029 A036833 * A009242 A032647 A327165
KEYWORD
nonn
AUTHOR
Michel Marcus, Nov 03 2014
STATUS
approved