A322021 Lexicographically earliest such sequence a that a(i) = a(j) => A046523(i) = A046523(j) and A048250(i) = A048250(j), for all i, j.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 14, 15, 16, 12, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 26, 42, 43, 44, 45, 18, 42, 46, 47, 22, 42, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 54, 58, 61, 62, 63, 64, 26, 65, 54, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 52, 78, 79, 80, 81, 75, 82, 83, 26

Offset: 1

Author

Antti Karttunen, Nov 29 2018

Keywords

• nonn

Comments

Restricted growth sequence transform of A291758, which means that this is the lexicographically least sequence a, such that for all i, j: a(i) = a(j) <=> A291758(i) = A291758(j) <=> A046523(i) = A046523(j) and A048250(i) = A048250(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.

For all i, j:

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

a(i) = a(j) => A304411(i) = A304411(j),

a(i) = a(j) => A304412(i) = A304412(j).

Links

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

Crossrefs

Cf. A046523, A048250, A291751, A291758, A294877, A295300, A322022.

Cf. also A304411, A304412.

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; };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
A048250(n) = if(n<1, 0, sumdiv(n, d, if(core(d)==d, d)));
v322021 = rgs_transform(vector(up_to, n, [A046523(n), A048250(n)]));
A322021(n) = v322021[n];