A304755 Suspected divisor-or-multiple permutation: a(1) = 1, and for n > 1, a(n) is either the second smallest divisor of a(n-1) not already present in sequence, or the smallest divisor if it is the only one not yet used, or (if all divisors have been already encountered), a(n) = a(n-1) * {the least power of the least prime not dividing a(n-1) such that the term is not already present}.

1, 2, 6, 3, 12, 4, 36, 18, 9, 72, 24, 8, 216, 54, 27, 108, 540, 10, 5, 20, 60, 30, 15, 120, 40, 360, 90, 45, 180, 1260, 14, 7, 28, 84, 42, 21, 168, 56, 504, 126, 63, 252, 6300, 35, 70, 210, 105, 420, 140, 3780, 189, 378, 1890, 270, 135, 1080, 7560, 315, 630, 6930, 22, 11, 44, 132, 66, 33, 264, 88, 792, 198, 99, 396, 1980, 110, 55

Offset: 1

Author

Antti Karttunen, May 20 2018

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A304756 (inverse).

Cf. A053669, A304757.

Cf. A303751, also A282291, A304531 for variants.

Programs

PARI

up_to = 2^16;
A053669(n) = forprime(p=2, , if (n % p, return(p))); \\ From A053669
v304755 = vector(up_to);
m304756 = Map();
find_kth_unused_divisor(k,n,m_inverses) = { my(pd=0); fordiv(n,d,if(!mapisdefined(m_inverses,d),pd=d;k--); if((!k || (d == n)), return(pd))); };
prev=1; for(n=1,up_to, if((try = find_kth_unused_divisor(2,prev,m304756))!=0, mapput(m304756,v304755[n] = try,n), p = A053669(prev); while(mapisdefined(m304756,prev), prev *= p); v304755[n] = prev; mapput(m304756,prev,n)); prev = v304755[n]);
A304755(n) = v304755[n];
A304756(n) = mapget(m304756,n);