cp's OEIS Frontend

A303761 Divisor-or-multiple permutation of squarefree numbers: a(0) = 1, and for n >= 1, a(n) is either the least divisor of a(n-1) not already present, or (if all divisors already used), a(n) is obtained by iterating the map x -> x*A053669(x), starting from x = a(n-1), until x is found which is not already present in the sequence.

%I A303761 #25 May 04 2018 22:38:23
%S A303761 1,2,6,3,30,5,10,210,7,14,42,21,2310,11,22,66,33,330,15,30030,13,26,
%T A303761 78,39,390,65,130,2730,35,70,510510,17,34,102,51,510,85,170,3570,105,
%U A303761 9699690,19,38,114,57,570,95,190,3990,133,266,798,399,43890,55,110,223092870,23,46,138,69,690,115,230,4830,161,322,966,483,53130,77
%N A303761 Divisor-or-multiple permutation of squarefree numbers: a(0) = 1, and for n >= 1, a(n) is either the least divisor of a(n-1) not already present, or (if all divisors already used), a(n) is obtained by iterating the map x -> x*A053669(x), starting from x = a(n-1), until x is found which is not already present in the sequence.
%C A303761 Each a(n+1) is either a divisor or a multiple of a(n).
%C A303761 The primorials (A002110) occur in ascending order, in positions given by A300829, and each is then followed by the least unused term up to that point. For n = 2 .. 79 this is the highest prime factor of the said primorial, but note that for A300829(80) = 4965, a(4965) = A002110(80), but a(4966) = 407 = 11*37, instead of prime(80) = 409. Note that 409 occurs at a(5043), where 5043 = 1+A300829(81).
%C A303761 For example, 11 comes after a(A300829(5)) = a(12) = 2310 = 2*3*5*7*11, and all squarefree numbers < 11: {1, 2, 3, 5, 6, 7, 10} occur before a(13).
%H A303761 Antti Karttunen, <a href="/A303761/b303761.txt">Table of n, a(n) for n = 0..4095</a>
%F A303761 a(n) = A019565(A303765(n)).
%F A303761 For n >= 0, a(A300829(n)) = A002110(n) [primorials are the records].
%F A303761 For n = 2 .. 79, a(1+A300829(n)) = A000040(n).
%o A303761 (PARI)
%o A303761 default(parisizemax,2^31);
%o A303761 up_to = 2^8;
%o A303761 A053669(n) = forprime(p=2, , if (n % p, return(p))); \\ From A053669
%o A303761 v303761 = vector(up_to);
%o A303761 m_inverses = Map();
%o A303761 prev=1;for(n=1,up_to,fordiv(prev,d,if(!mapisdefined(m_inverses,d),v303761[n] = d;mapput(m_inverses,d,n);break)); if(!v303761[n], while(mapisdefined(m_inverses,prev), prev *= A053669(prev)); v303761[n] = prev; mapput(m_inverses,prev,n)); prev = v303761[n]);
%o A303761 A303761(n) = v303761[n+1];
%Y A303761 Cf. A005117, A019565, A053669, A300829 (gives the positions of records), A303765.
%Y A303761 Cf. also A303751, A303760, A303762.
%K A303761 nonn
%O A303761 0,2
%A A303761 _Antti Karttunen_, May 02 2018