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

0,2

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

Formula

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

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

Prog

(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));

Crossrefs

Cf. A302784 (inverse).

Cf. A006068, A050376, A052330, A302777.

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

Sequence in context: A206493 A359256 A304085 * A364318 A008306 A231171

Adjacent sequences: A302780 A302781 A302782 * A302784 A302785 A302786

Keyword

nonn

Author

Antti Karttunen, Apr 16 2018

Status

approved