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 A120359 Even refactorable numbers k such that the number r of odd divisors is odd, the number s of even divisors is even, both r and s are divisors of k and k is the first number for which the triple (r,s,t) occurs, where t is the number of divisors of k. 3
 36, 3600, 8100, 10000, 26244, 32400, 142884, 202500, 396900, 518400, 656100, 810000, 1587600, 1679616, 2286144, 2624400, 3572100, 6350400, 9144576, 9922500, 12960000, 14288400, 20575296, 25401600, 28579716, 32148900, 39690000, 41990400, 48024900, 57153600, 89302500 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Note that s is necessarily a multiple of r. LINKS Table of n, a(n) for n=1..31. EXAMPLE a(1) = 36 since r = 3, s = 6 and t = r+s = 9. MATHEMATICA seq[kmax_] := Module[{triples = {}, v = {}, r, s, t}, Do[t = DivisorSigma[0, k]; r = t - DivisorSigma[0, k/2]; s = t - r; If[OddQ[r] && EvenQ[s] && FreeQ[triples, {r, s, t}] && Divisible[k, t] && Divisible[k, r] && Divisible[k, s], AppendTo[v, k]; AppendTo[triples, {r, s, t}]], {k, 2, kmax, 2}]; v]; seq[10^6] (* Amiram Eldar, Aug 01 2024 *) CROSSREFS Cf. A000005, A001227, A033950, A049439, A057265, A120358, A120361, A183063. Sequence in context: A364175 A209267 A120349 * A194611 A165984 A297021 Adjacent sequences: A120356 A120357 A120358 * A120360 A120361 A120362 KEYWORD nonn AUTHOR Walter Kehowski, Jun 25 2006 EXTENSIONS a(21)-a(22) inserted and a(24)-a(31) added by Amiram Eldar, Aug 01 2024 STATUS approved

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Last modified September 14 13:32 EDT 2024. Contains 375921 sequences. (Running on oeis4.)