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 A335216 Bi-unitary Zumkeller numbers (A335215) that are not exponentially odd numbers (A268335). 1
 48, 60, 72, 80, 90, 150, 162, 192, 240, 288, 294, 320, 336, 360, 420, 432, 448, 504, 528, 540, 560, 576, 600, 624, 630, 648, 660, 720, 726, 756, 768, 780, 792, 800, 810, 816, 832, 880, 912, 924, 936, 960, 990, 1008, 1014, 1020, 1040, 1050, 1092, 1104, 1134, 1140 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Zumkeller numbers (A083207) that are exponentially odd (A268335) are also bi-unitary Zumkeller numbers (A335215), since all of their divisors are bi-unitary. LINKS Table of n, a(n) for n=1..52. EXAMPLE 48 is a term since it is not exponentially odd number (48 = 2^4 * 3 and 4 is even), and its set of bi-unitary divisors, {1, 2, 3, 6, 8, 16, 24, 48}, can be partitioned into 2 disjoint sets, whose sum is equal: 1 + 2 + 3 + 8 + 16 + 24 = 6 + 48. MATHEMATICA uDivs[n_] := Select[Divisors[n], CoprimeQ[#, n/#] &]; bDivs[n_] := Select[Divisors[n], Last @ Intersection[uDivs[#], uDivs[n/#]] == 1 &]; bzQ[n_] := Module[{d = bDivs[n], sum, x}, sum = Plus @@ d; If[sum < 2*n || OddQ[sum], False, CoefficientList[Product[1 + x^i, {i, d}], x][[1 + sum/2]] > 0]]; expOddQ[n_] := AllTrue[Last /@ FactorInteger[n], OddQ]; Select[Range[1000], !expOddQ[#] && bzQ[#] &] CROSSREFS Subsequence of A335215. Cf. A083207, A268335, A290466. Sequence in context: A231469 A261546 A335938 * A114821 A108098 A114505 Adjacent sequences: A335213 A335214 A335215 * A335217 A335218 A335219 KEYWORD nonn AUTHOR Amiram Eldar, May 27 2020 STATUS approved

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Last modified September 18 19:41 EDT 2024. Contains 376002 sequences. (Running on oeis4.)