A294877 Lexicographically earliest such sequence a that a(i) = a(j) => A003557(i) = A003557(j) and A046523(i) = A046523(j), for all i, j.

1, 2, 2, 3, 2, 4, 2, 5, 6, 4, 2, 7, 2, 4, 4, 8, 2, 9, 2, 7, 4, 4, 2, 10, 11, 4, 12, 7, 2, 13, 2, 14, 4, 4, 4, 15, 2, 4, 4, 10, 2, 13, 2, 7, 9, 4, 2, 16, 17, 18, 4, 7, 2, 19, 4, 10, 4, 4, 2, 20, 2, 4, 9, 21, 4, 13, 2, 7, 4, 13, 2, 22, 2, 4, 18, 7, 4, 13, 2, 16, 23, 4, 2, 20, 4, 4, 4, 10, 2, 24, 4, 7, 4, 4, 4, 25, 2, 26, 9, 27, 2, 13, 2, 10, 13, 4, 2, 28, 2, 13

Offset: 1

Author

Antti Karttunen, Nov 11 2017

Keywords

• nonn

Comments

Restricted growth sequence transform of A291757, which means that this is the lexicographically least sequence a, such that for all i, j: a(i) = a(j) <=> A291757(i) = A291757(j) <=> A003557(i) = A003557(j) and A046523(i) = A046523(j). That this is equal to the definition given in the title follows because any such lexicographically least sequence satisfying relation <=> is also the least sequence satisfying relation => with the same parameters.

Also the restricted growth sequence transform of A294876, Product_{d|n, d>1} prime(gcd(d,n/d)). (This was the original definition).

For all i, j:

A295300(i) = A295300(j) => a(i) = a(j),

A319347(i) = A319347(j) => a(i) = a(j),

a(i) = a(j) => A055155(i) = A055155(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. also A291751, A291757, A294876, A295300, A295888, A319347, A322021.

Cf. A000188, A055155, A294897, A295666, A322020 (a few of the matched sequences).

Programs

PARI

up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A294876(n) = { my(m=1); fordiv(n,d,if(d>1, m *= prime(gcd(d,n/d)))); m; };
v294877 = rgs_transform(vector(up_to,n,A294876(n)));
A294877(n) = v294877[n];

PARI

A003557(n) = n/factorback(factor(n)[, 1]); \\ From A003557
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
v294877 = rgs_transform(vector(up_to,n,[A003557(n),A046523(n)]));
A294877(n) = v294877[n]; \\ Antti Karttunen, Nov 28 2018

Extensions

Name changed and comments added by Antti Karttunen, Nov 28 2018