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A177899
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Nonsquarefree numbers that are not in A177880.
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1
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8, 16, 24, 27, 40, 48, 54, 56, 80, 81, 88, 104, 112, 120, 125, 135, 136, 152, 162, 168, 176, 184, 189, 208, 216, 232, 240, 248, 250, 264, 270, 272, 280, 296, 297, 304, 312, 328, 336, 343, 344, 351, 368, 375, 376, 378, 405, 408, 424, 432, 440, 456, 459, 464, 472, 488, 496, 512, 513, 520, 528, 536
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OFFSET
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1,1
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LINKS
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FORMULA
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Let B(x) be the counting function for terms not exceeding x. Then for x tends to infinity, B(x)=C*x+o(x^(0.5+eps), where C = Product_{i=p^(3^k) with prime p and k>=0}(1-1/(i^2+i+1)) - 1/zeta(2).
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MAPLE
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isA005836 := proc(n) convert(convert(n, base, 3), set) intersect {2} ; % = {} ; end proc:
isA177880 := proc(n) local f; for f in ifactors(n)[2] do if not isA005836(op(2, f)) then return true; end if; end do: return false; end proc:
isA177899 := proc(n) not numtheory[issqrfree](n) and not isA177880(n) ; end proc:
for n from 1 to 1000 do if isA177899(n) then printf("%d, ", n) ; end if; end do: # R. J. Mathar, Dec 20 2010
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MATHEMATICA
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Select[Range[500], AnyTrue[(e = FactorInteger[#][[;; , 2]]), #1 > 1 &] && AllTrue[e, DigitCount[#1, 3, 2] == 0 &] &] (* Amiram Eldar, Aug 31 2020 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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