A304085 Divisor-or-multiple permutation of natural numbers: a(n) = A052330(A304083(n)).

1, 2, 6, 3, 24, 12, 4, 8, 120, 60, 20, 5, 40, 10, 30, 15, 840, 420, 140, 35, 7, 280, 70, 14, 210, 105, 21, 168, 84, 28, 56, 7560, 42, 1890, 945, 315, 63, 9, 3780, 1260, 252, 36, 2520, 630, 126, 18, 1512, 756, 189, 27, 378, 54, 1080, 540, 180, 45, 360, 90, 270, 135, 83160, 504, 72, 216, 108, 41580, 13860, 3465, 693, 99, 11, 27720, 6930, 1386, 198, 22, 20790

Offset: 0

Author

Antti Karttunen, May 06 2018

Keywords

• nonn

Comments

Each a(n) is always either a divisor or a multiple of a(n+1).

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16383
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A304086 (inverse).

Cf. A304083, A304087.

Cf. also A064736, A113552, A207901, A281978, A282291, A302350, A302781, A302783, A303751, A303771 for similar permutations.

Programs

PARI

up_to_e = 16; \\ Good for computing up to n = (2^16)-1
v050376 = vector(up_to_e);
ispow2(n) = (n && !bitand(n,n-1));
i = 0; for(n=1,oo,if(ispow2(isprimepower(n)), i++; v050376[i] = n); if(i == up_to_e,break));
A050376(n) = v050376[n];
A052330(n) = { my(p=1,i=1); while(n>0, if(n%2, p *= A050376(i)); i++; n >>= 1); (p); };
A304085(n) = A052330(A304083(n)); \\ Needs also code from A304083

Formula

a(n) = A052330(A304083(n)).