%I #25 Nov 11 2024 22:23:38

%S 1,6,12,28,30,2,56,120,117,45,132,21,182,84,40,496,306,78,380,210,672,

%T 198,552,10,775,273,1080,2,870,60,992,2016,176,459,1680,3276,1406,570,

%U 2184,36,1722,112,1892,231,390,828,2256,372,2793,4650,408,1274,2862

%N a(n) = A017665(n)*A017666(n).

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

%H Allan C. Wechsler, <a href="/A249670/b249670.txt">Table of n, a(n) for n = 1..10000</a>

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

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

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

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

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

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

%o (Haskell)

%o a249670 n = div (n * s) (gcd n s ^ 2)

%o where s = sum (filter (\k -> mod n k == 0) [1..n])

%o -- _Allan C. Wechsler_, Mar 31 2023

%Y Cf. A000203 (sigma(n)).

%Y Cf. A017665/A017666 (abundancy of n).

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

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

%K nonn

%O 1,2

%A _Michel Marcus_, Nov 03 2014