A177899 Nonsquarefree numbers that are not in A177880.
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
Offset: 1
Keywords
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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Maple
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
Select[Range[500], AnyTrue[(e = FactorInteger[#][[;; , 2]]), #1 > 1 &] && AllTrue[e, DigitCount[#1, 3, 2] == 0 &] &] (* Amiram Eldar, Aug 31 2020 *)
Formula
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).