A302783 - OEIS

%I #17 Apr 17 2018 18:29:49

%S 1,2,6,3,24,12,4,8,120,60,20,40,5,10,30,15,840,420,140,280,35,70,210,

%T 105,7,14,42,21,168,84,28,56,7560,3780,1260,2520,315,630,1890,945,63,

%U 126,378,189,1512,756,252,504,9,18,54,27,216,108,36,72,1080,540,180,360,45,90,270,135,83160,41580,13860,27720,3465,6930,20790,10395,693

%N A divisor-or-multiple permutation of natural numbers: a(n) = A052330(A006068(n)).

%C Shares with A064736, A207901, A302781, A302350, etc. a property that a(n) is always either a divisor or a multiple of a(n+1). However, because multiple bits may change simultaneously when moving from A006068(n) to A006068(n+1) [with the restriction that the changing bits are all either toggled on or all toggled off], it means that also here the terms might be divided or multiplied by more than just a single Fermi-Dirac prime (A050376). E.g. a(3) = 3, while a(4) = A050376(1) * A050376(3) * 3 = 2*4*3 = 24. See also comments in A284003.

%H Antti Karttunen, <a href="/A302783/b302783.txt">Table of n, a(n) for n = 0..8191</a>

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F a(n) = A052330(A006068(n)).

%F a(n) = A207901(A064707(n)).

%o (PARI)

%o up_to_e = 13;

%o v050376 = vector(up_to_e);

%o A050376(n) = v050376[n];

%o A209229(n) = (n && !bitand(n,n-1));

%o A302777(n) = A209229(isprimepower(n));

%o i = 0; for(n=1,oo,if(A302777(n), i++; v050376[i] = n); if(i == up_to_e,break));

%o A052330(n) = { my(p=1,i=1); while(n>0, if(n%2, p *= A050376(i)); i++; n >>= 1); (p); };

%o A006068(n)= { my(s=1, ns); while(1, ns = n >> s; if(0==ns, break()); n = bitxor(n, ns); s <<= 1; ); return (n); } \\ From A006068

%o A302783(n) = A052330(A006068(n));

%Y Cf. A302784 (inverse).

%Y Cf. A006068, A050376, A052330, A302777.

%Y Cf. also A207901 and A284003 (a squarefree analog).

%K nonn

%O 0,2

%A _Antti Karttunen_, Apr 16 2018