A302783 A divisor-or-multiple permutation of natural numbers: a(n) = A052330(A006068(n)).

1, 2, 6, 3, 24, 12, 4, 8, 120, 60, 20, 40, 5, 10, 30, 15, 840, 420, 140, 280, 35, 70, 210, 105, 7, 14, 42, 21, 168, 84, 28, 56, 7560, 3780, 1260, 2520, 315, 630, 1890, 945, 63, 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

Offset: 0

Author

Antti Karttunen, Apr 16 2018

Keywords

• nonn

Comments

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.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..8191
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A302784 (inverse).

Cf. A006068, A050376, A052330, A302777.

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

Programs

PARI

up_to_e = 13;
v050376 = vector(up_to_e);
A050376(n) = v050376[n];
A209229(n) = (n && !bitand(n,n-1));
A302777(n) = A209229(isprimepower(n));
i = 0; for(n=1,oo,if(A302777(n), i++; v050376[i] = n); if(i == up_to_e,break));
A052330(n) = { my(p=1,i=1); while(n>0, if(n%2, p *= A050376(i)); i++; n >>= 1); (p); };
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
A302783(n) = A052330(A006068(n));

Formula

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

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