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 A120360 Even refactorable numbers k such that the number of odd divisors of k and the number of even divisors of k are both even divisors of k. 1
 12, 24, 80, 180, 240, 252, 360, 396, 468, 480, 504, 560, 612, 684, 720, 792, 828, 880, 896, 936, 972, 1040, 1044, 1116, 1200, 1224, 1332, 1344, 1360, 1368, 1440, 1476, 1520, 1548, 1620, 1656, 1692, 1840, 1908, 1944, 2000, 2088, 2124, 2196, 2232, 2320 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Note that the number of even divisors s is necessarily a multiple of the number of odd divisors r. LINKS Amiram Eldar, Table of n, a(n) for n = 1..10000 EXAMPLE a(1) = 12 since r = 2, s = 4, t = r + s = 6. MATHEMATICA oddtau[n_] := DivisorSigma[0, n/2^IntegerExponent[n, 2]]; seqQ[n_] := Module[{d = DivisorSigma[0, n], o = odd[n]}, EvenQ[d] && EvenQ[o] && Divisible[n, d] && Divisible[n, o] && Divisible[n, d - o]]; Select[Range[2, 2320, 2], seqQ] (* Amiram Eldar, Jan 15 2020 *) CROSSREFS Cf. A033950, A049439, A057265, A120350. Sequence in context: A001041 A216425 A081751 * A120356 A109745 A364726 Adjacent sequences: A120357 A120358 A120359 * A120361 A120362 A120363 KEYWORD nonn AUTHOR Walter Kehowski, Jun 25 2006 STATUS approved

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Last modified September 30 18:42 EDT 2023. Contains 365793 sequences. (Running on oeis4.)