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

%I A249670 #25 Nov 11 2024 22:23:38
%S A249670 1,6,12,28,30,2,56,120,117,45,132,21,182,84,40,496,306,78,380,210,672,
%T A249670 198,552,10,775,273,1080,2,870,60,992,2016,176,459,1680,3276,1406,570,
%U A249670 2184,36,1722,112,1892,231,390,828,2256,372,2793,4650,408,1274,2862
%N A249670 a(n) = A017665(n)*A017666(n).
%C A249670 If n is a k-multiperfect, then a(n) = k.
%H A249670 Allan C. Wechsler, <a href="/A249670/b249670.txt">Table of n, a(n) for n = 1..10000</a>
%F A249670 a(n) = A064987(n)/A009194(n)^2.
%F A249670 a(A000396(n)) = 2 (perfect).
%F A249670 a(A005820(n)) = 3 (tri-perfect).
%F A249670 For p prime, a(p) = p*(p+1).
%t A249670 a249670[n_Integer] := Numerator[DivisorSigma[-1, n]]*Denominator[DivisorSigma[-1, n]]; a249670 /@ Range[80] (* _Michael De Vlieger_, Nov 10 2014 *)
%o A249670 (PARI) a(n) = my(ab = sigma(n)/n); numerator(ab)*denominator(ab);
%o A249670 (Haskell)
%o A249670 a249670 n = div (n * s) (gcd n s ^ 2)
%o A249670  where s = sum (filter (\k -> mod n k == 0) [1..n])
%o A249670 -- _Allan C. Wechsler_, Mar 31 2023
%Y A249670 Cf. A000203 (sigma(n)).
%Y A249670 Cf. A017665/A017666 (abundancy of n).
%Y A249670 Cf. A009194 (gcd(n, sigma(n))), A064987 (n*sigma(n)).
%Y A249670 Cf. A000396, A005820, A027687, A046060, A046061.
%K A249670 nonn
%O A249670 1,2
%A A249670 _Michel Marcus_, Nov 03 2014