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A196747 Numbers n such that 3 does not divide swing(n) = A056040(n).

%I A196747 #18 Aug 24 2016 11:56:44
%S A196747 0,1,2,6,7,8,18,19,20,24,25,26,54,55,56,60,61,62,72,73,74,78,79,80,
%T A196747 162,163,164,168,169,170,180,181,182,186,187,188,216,217,218,222,223,
%U A196747 224,234,235,236,240,241,242,486,487,488,492,493,494,504,505,506,510
%N A196747 Numbers n such that 3 does not divide swing(n) = A056040(n).
%H A196747 Charles R Greathouse IV, <a href="/A196747/b196747.txt">Table of n, a(n) for n = 1..10000</a>
%H A196747 Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/PrimeFactorsSwingingFactorial">On the prime factors of the swinging factorial</a>.
%p A196747 SwingExp := proc(m,n) local p, q; p := m;
%p A196747 do q := iquo(n,p);
%p A196747    if (q mod 2) = 1 then RETURN(1) fi;
%p A196747    if q = 0 then RETURN(0) fi;
%p A196747    p := p * m;
%p A196747 od end:
%p A196747 Search := proc(n,L) local m, i, r; m := n;
%p A196747 for i in L do r := SwingExp(i,m);
%p A196747    if r <> 0 then RETURN(NULL) fi
%p A196747 od; n end:
%p A196747 A196747_list := n -> Search(n,[3]):  # n is a search limit
%t A196747 (* A naive solution *) sf[n_] := n!/Quotient[n, 2]!^2; Select[Range[0, 600], ! Divisible[sf[#], 3] &] (* _Jean-François Alcover_, Jun 28 2013 *)
%o A196747 (PARI) valp(n,p)=my(s); while(n\=p, s+=n); s
%o A196747 is(n)=my(t=valp(n,3)); t%2==0 && 2*valp(n\2,3)==t \\ _Charles R Greathouse IV_, Feb 02 2016
%Y A196747 Cf. A005836, A129508, A030979, A151750, A196748, A196749, A196750.
%K A196747 nonn
%O A196747 1,3
%A A196747 _Peter Luschny_, Oct 06 2011