A196748 Numbers n such that 3 and 5 do not divide swing(n) = A056040(n).

0, 1, 2, 20, 24, 54, 60, 61, 62, 72, 73, 74, 504, 510, 511, 512, 560, 564, 1512, 1513, 1514, 1520, 1620, 1621, 1622, 6320, 6324, 6372, 6373, 6374, 6500, 6504, 6552, 6553, 6554, 6560, 13122, 13123, 13124, 13770, 13771, 13772, 13824, 13850, 15072, 15073, 15074

Offset: 1

Author

Peter Luschny, Oct 06 2011

Keywords

• nonn

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..1000
• P. Erdos, R. L. Graham, I. Z. Russa and E. G. Straus, On the prime factors of C(2n,n), Math. Comp. 29 (1975), 83-92.
• Peter Luschny, On the prime factors of the swinging factorial.

Crossrefs

Cf. A005836, A129508, A030979, A151750, A196747, A196749, A196750.

Programs

Maple

# The function Search is defined in A196747.
A196748_list := n -> Search(n,[3,5]):  # n is a search limit

Mathematica

(* 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 *)

PARI

valp(n,p)=my(s); while(n\=p, s+=n); s
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