Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #15 Feb 03 2016 11:38:32
%S 0,1,2,20,24,54,60,61,62,72,73,74,504,510,511,512,560,564,1512,1513,
%T 1514,1520,1620,1621,1622,6320,6324,6372,6373,6374,6500,6504,6552,
%U 6553,6554,6560,13122,13123,13124,13770,13771,13772,13824,13850,15072,15073,15074
%N Numbers n such that 3 and 5 do not divide swing(n) = A056040(n).
%H Charles R Greathouse IV, <a href="/A196748/b196748.txt">Table of n, a(n) for n = 1..1000</a>
%H P. Erdos, R. L. Graham, I. Z. Russa and E. G. Straus, <a href="http://www.math.ucsd.edu/~ronspubs/75_03_prime_factors.pdf">On the prime factors of C(2n,n)</a>, Math. Comp. 29 (1975), 83-92.
%H Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/PrimeFactorsSwingingFactorial">On the prime factors of the swinging factorial</a>.
%p # The function Search is defined in A196747.
%p A196748_list := n -> Search(n,[3,5]): # n is a search limit
%t (* A naive solution *) sf[n_] := n!/Quotient[n, 2]!^2; Select[Range[0, 16000], !Divisible[sf[#], 3] && !Divisible[sf[#], 5] &] (* _Jean-François Alcover_, Jun 28 2013 *)
%o (PARI) valp(n,p)=my(s); while(n\=p, s+=n); s
%o is(n)=valp(n,3)==2*valp(n\2,3) && valp(n,5)==2*valp(n\2,5) \\ _Charles R Greathouse IV_, Feb 02 2016
%Y Cf. A005836, A129508, A030979, A151750, A196747, A196749, A196750.
%K nonn
%O 1,3
%A _Peter Luschny_, Oct 06 2011